Measure π | CompData | 3061 mathmath: exists_pos_preimage_ball, ProbabilityTheory.Kernel.restrict_apply', Measure.prod_apply_symm, AddCircle.measure_univ, predictablePart_add_ae_eq, exists_lt_lowerSemicontinuous_integral_gt_nnreal, Measure.comap_undef, Measure.MeasureDense.approx, Integrable.measure_norm_gt_lt_top_enorm, AEEqFun.coeFn_smul, Measure.univ_pi_Ioc_ae_eq_Icc, StronglyMeasurable.integral_kernel_prod_right'', Measure.MutuallySingular.smul_nnreal, LpToLpRestrictCLM_coeFn, SMulInvariantMeasure.smul, Measure.IsHaarMeasure.nnreal_smul, Measure.InnerRegular.instHAdd, VitaliFamily.FineSubfamilyOn.measure_diff_biUnion, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, vaddInvariantMeasure_iff, ProbabilityTheory.Kernel.prod_apply', SignedMeasure.toMeasureOfZeroLE_apply, ProbabilityTheory.Kernel.tendsto_m_density, MeasurableEmbedding.comap_add, ProbabilityTheory.absolutelyContinuous_posterior_iff, Lp.mul_meas_ge_le_pow_enorm', ProbabilityTheory.Kernel.sectR_apply, llr_self, StieltjesFunction.measure_univ_of_tendsto_atBot_atBot, Measure.restrict_singleton, IsZeroOrProbabilityMeasure.measure_univ, ProbabilityTheory.Kernel.coe_nsmul, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, Measure.isAddInvariant_eq_smul_of_compactSpace, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.condCDF_ae_eq, Measure.sum_apply_eq_zero', ProbabilityTheory.Kernel.iIndepSet_iff_meas_biInter, lintegral_add_measure, IsAddFundamentalDomain.measure_addFundamentalInterior, ae_withDensity_iff_ae_restrict, ProbabilityTheory.lintegral_condCDF, Measure.rnDeriv_zero, Measure.addHaar_eq_zero_of_disjoint_translates, MonotoneOn.ae_differentiableWithinAt_of_mem, SimpleFunc.sum_measure_preimage_singleton, iInf_mul_le_lintegral, Measure.addHaar_image_continuousLinearMap, withDensity_apply_le, Martingale.stoppedValue_ae_eq_restrict_eq, Measure.IsEverywherePos.smul_measure, ProbabilityTheory.condDistrib_apply_of_ne_zero, forall_measure_preimage_add_iff, PMF.toMeasure_pure_apply, ProbabilityTheory.condDistrib_ae_eq_condExp, restrict_dirac', coe_measureUnivNNReal, ProbabilityTheory.Kernel.lintegral_swapRight, ProbabilityMeasure.coe_mk, aeconst_of_dense_aestabilizer_smul, condExpInd_ae_eq_condExpIndSMul, Measure.le_comap_apply, Measure.addHaar_sphere, hausdorffMeasure_segment, Measure.join_smul, InnerProductSpace.volume_closedBall_of_dim_even, lintegral_const, Measure.restrict_smul, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, Measure.ae_ennreal_smul_measure_eq, measure_sdiff_inv_smul, integral_smul_nnreal_measure, isFiniteMeasureAdd, condExp_bilin_of_stronglyMeasurable_left, Real.smul_map_volume_mul_right, Integrable.measure_enorm_ge_lt_top, Measure.haar_singleton, unitInterval.volume_Ioo, unitInterval.volume_Iic, AEStronglyMeasurable.integral_condDistrib_map, Measure.IsAddHaarMeasure.smul, isFiniteMeasureZero, Measure.sub_top, measure_of_cont_bdd_of_tendsto_indicator, Measure.jordanDecompositionOfToSignedMeasureSub_posPart, Measure.swap_comp, AEEqFun.compβMeasurable_toGerm, instIsFiniteMeasureSumMeasure, Measure.WeaklyRegular.smul_nnreal, Integrable.toL1_eq_toL1_iff, ProbabilityTheory.lintegral_toKernel_univ, Measure.AbsolutelyContinuous.smul_left, Measure.rnDeriv_smul_right', eLpNorm'_const', unifIntegrable_zero_meas, lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, volume_iUnion_setOf_liouvilleWith, Submartingale.upcrossings_ae_lt_top, hasFiniteIntegral_zero_measure, ProbabilityTheory.condIndep_iff, IsAddFoelner.eventually_meas_ne_top, StieltjesFunction.measure_botSet, SimpleFunc.measure_support_lt_top_of_integrable, Integrable.withDensityα΅₯_eq_iff, ContinuousMap.coeFn_toAEEqFun, Lp.simpleFunc.toSimpleFunc_indicatorConst, Measure.hausdorffMeasure_zero_singleton, AntilipschitzWith.hausdorffMeasure_preimage_le, Measure.WeaklyRegular.zero, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', lintegral_eq_zero_iff, ProbabilityTheory.Kernel.iIndep.meas_biInter, VectorMeasure.equivMeasure_apply, vadd_ae, ProbabilityTheory.IsRatCondKernelCDF.iInf_rat_gt_eq, integral_domSMul, DominatedFinMeasAdditive.add_measure_left, ProbabilityTheory.Kernel.density_fst_univ, ProbabilityTheory.Kernel.setIntegral_deterministic', AbsolutelyContinuousOnInterval.ae_differentiableAt, Measure.ext_iff, ContinuousLinearMap.comp_condExp_comm, Measure.rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular, ProbabilityTheory.setLIntegral_preCDF_fst, VitaliFamily.withDensity_le_mul, pdf.uniformPDF_ite, Measure.conv_zero, MeasuredSets.sub_le_edist, StieltjesFunction.measure_zero, Measure.lintegral_rnDeriv, ProbabilityTheory.Kernel.map_apply, LipschitzOnWith.ae_differentiableWithinAt_of_mem, measure_compl_sigmaFiniteSet, ae_le_const_iff_forall_gt_measure_zero, NullMeasurableSet.exists_isOpen_symmDiff_lt, setLIntegral_le_iSup_mul, measure_le_lintegral_thickenedIndicatorAux, Measure.rnDeriv_mul_rnDeriv', VitaliFamily.le_mul_withDensity, Measure.outerMeasure_le_iff, PMF.toMeasure_bind_apply, MeasurableEmbedding.rnDeriv_map, AEEqFun.toGerm_injective, ProbabilityTheory.Kernel.condExp_traj', AddCircle.volume_eq_smul_haarAddCircle, Lp.coeFn_add, Measure.pi_Ioc_ae_eq_pi_Icc, Measure.AbsolutelyContinuous.kernel_of_compProd, ProbabilityTheory.iIndepFun_iff, addHaarScalarFactor_smul_inv_eq_distribHaarChar, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, PMF.toMeasure_ofFinset_apply, Measure.rnDeriv_add_of_mutuallySingular, measure_eq_top_of_subset_compl_sigmaFiniteSetWRT'_of_measurableSet, Measure.inv_rnDeriv', Lp.eq_zero_iff_ae_eq_zero, StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTop, LocallyIntegrable.ae_hasDerivAt_integral, ProbabilityTheory.iIndep.meas_biInter, Measure.mutuallySingular_tfae, ae_eq_const_or_exists_average_ne_compl, measure_eq_top_iff_of_symmDiff, Measure.measure_isMulLeftInvariant_eq_smul_of_ne_top, Measure.count_injective_image', Lp.ext_iff, ae_restrict_mem, measure_inv_null, condLExp_add_right, measure_biUnion, setLIntegral_pos_iff, Measure.comp_apply_univ, ProbabilityTheory.Kernel.swapRight_apply', UniformIntegrable.uniformIntegrable_of_ae_tendsto, LipschitzWith.ae_lineDeriv_sum_eq, ProbabilityTheory.condExp_ae_eq_integral_condDistrib_id, isTightMeasureSet_iff_inner_tendsto, Measurable.lintegral_kernel_prod_left', Measure.measure_subtype_coe_le_comap, ProbabilityMeasure.toMeasure_add_pos_gt_mem_nhds, Filter.HasBasis.notMem_measureSupport, Measure.AbsolutelyContinuous.add_left, Measure.comp_add, smul_le_stoppedValue_hittingBtwn, Lp.coeFn_const, Measure.measure_toMeasurable_add_inter_right, ProbabilityTheory.rnDeriv_gaussianReal, measure_le_setLAverage_pos, ae_eq_zero_restrict_of_forall_setIntegral_eq_zero_real, Integrable.norm_integral_condExpKernel, Measure.map_add, measure_preimage_mul, integral_add_measure, Measure.instIsOrderedAddMonoid, Measure.toSphere_apply_aux, ProbabilityTheory.Kernel.coe_add, Measure.pi'_pi, measure_diff_le_iff_le_add, SimpleFunc.measure_support_lt_top_of_memLp, Integrable.measure_norm_ge_lt_top, ProbabilityTheory.Kernel.trajContent_cylinder, IsOpen.measure_eq_iSup_isClosed, tendsto_measure_iUnion_atBot, Measure.ae_mem_finset_iff, FinMeasAdditive.smul_measure, mem_ae_map_iff, AEEqFun.mk_le_mk, ProbabilityTheory.cond_apply, average_zero_measure, meas_le_lintegralβ, Measure.haarMeasure_closure_self, ProbabilityTheory.iIndepFun_iff_measure_inter_preimage_eq_mul, ProbabilityTheory.sum_prob_mem_Ioc_le, AEEqFun.coeFn_inf, Measure.measurable_measure, ProbabilityTheory.Kernel.indep_zero_right, measure_preimage_fst_singleton_eq_tsum, Measure.isTopologicalBasis_isOpen_lt_top, ProbabilityTheory.boolKernel_comp_measure, Measure.haarMeasure_apply, exp_llr_of_ac', measure_eq_measure_of_levyProkhorovEDist_eq_zero_of_isClosed, IsFundamentalDomain.measure_set_eq, Measure.singularPart_eq_zero, MeasurableEquiv.map_apply, ProbabilityTheory.Kernel.IndepSets.indep_aux, lintegral_indicator_one_le, AEEqFun.coeFn_mul, Measure.measure_univ_pos, LipschitzWith.ae_exists_fderiv_of_countable, AEEqFun.neg_toGerm, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, Ergodic.zero_measure, eLpNorm_const_lt_top_iff_enorm, lintegral_smul_measure, ProbabilityTheory.Kernel.setIntegral_restrict, Measure.restrict_empty, Measure.haveLebesgueDecompositionSMul, ContinuousLinearMap.comp_condExp_add_const_comm, Measure.ae_ne, ae_restrict_biUnion_iff, ProbabilityTheory.integrable_toReal_condExpKernel, ProbabilityTheory.Kernel.sectR_prodMkRight, toReal_rnDeriv_tilted_left, tilted_neg_same', AEEqFun.coeFn_compβ, Measure.le_ae_join, ProbabilityTheory.sum_meas_smul_cond_fiber, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_forall_memLp_exp_mul, ProbabilityTheory.IsRatCondKernelCDFAux.bddBelow_range, Measure.domSMul_apply, ProbabilityTheory.iIndepFun.measure_inter_preimage_eq_mul, condLExp_bot', AddContent.measure_eq, IsFoelner.eventually_meas_ne_zero, IsTightMeasureSet.union, LevyProkhorov.edist_measure_def, StieltjesFunction.measure_Ici_of_tendsto_atTop_atTop, Measure.coe_nnreal_smul_apply, Real.volume_closedEBall, Measure.comapβ_eq_comap, unitInterval.volume_Ico, measure_eq_top_of_setLIntegral_ne_top, lpMeasSubgroupToLpTrim_ae_eq, ProbabilityTheory.Kernel.integral_deterministic', measure_compl, MulAction.mem_aestabilizer, Measure.toSignedMeasure_le_toSignedMeasure_iff, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, Measure.comp_compProd_comm, measure_compl_sigmaFiniteSetWRT, restrict_compl_sigmaFiniteSet, Measure.haarMeasure_unique, Isometry.hausdorffMeasure_image, ProbabilityTheory.compProd_posterior_eq_map_swap, VitaliFamily.mul_measure_le_of_subset_lt_limRatioMeas, ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eq, ae_uIoc_iff, Measure.count_apply, ProbabilityTheory.Kernel.integral_restrict, addHaarScalarFactor_smul_eq_distribHaarChar_inv, Measure.instMeasurableAddβ, AEStronglyMeasurable.add_measure, condLExp_smul, MemLp.toLp_eq_toLp_iff, ae_eq_zero_of_integral_contMDiff_smul_eq_zero, StieltjesFunction.measure_Ioo, hasFiniteIntegral_prod_iff', Measure.measure_toMeasurable_add_inter_left, Measure.measure_preimage_neg, measure_support_eapprox_lt_top, Measure.restrict_add, ProbabilityTheory.bayesRisk_of_subsingleton', instSFiniteHAddMeasure, eLpNorm_smul_measure_of_ne_top', Measure.rnDeriv_smul_right, Measure.rnDeriv_smul_left_of_ne_top', ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_measure_eq_zero, ProbabilityTheory.uniformOn_inter, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, Measure.sum_smul_dirac, measure_eq_top_of_subset_compl_sigmaFiniteSetWRT', Measure.ae_mem_finset_iff_map_eq_sum_dirac, PMF.toMeasure_apply_singleton, LocallyBoundedVariationOn.ae_differentiableWithinAt, Directed.measure_iUnion, unitInterval.volume_apply, ProbabilityTheory.uniformOn_of_univ, isTightMeasureSet_singleton_of_innerRegularWRT, exists_measurable_supersetβ, Measure.le_sum_apply, ProbabilityTheory.Kernel.compProd_null, Real.volume_closedBall, ProbabilityTheory.tilted_mul_apply_cgf, Besicovitch.exists_closedBall_covering_tsum_measure_le, IsCompact.measure_closure, Measure.restrict_singleton', ProbabilityTheory.Kernel.lintegral_id_prod, setLIntegral_eq_const, Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub, IsOpen.measure_zero_iff_eq_empty, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, prob_compl_eq_one_iffβ, Measure.measurable_coe, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_comp_trim, Measure.restrict_apply_self, ae_restrict_biUnion_eq, pdf.eq_of_map_eq_withDensity, eventuallyConst_inv_set_ae, ProbabilityTheory.Kernel.nsmul_apply, ProbabilityTheory.setLIntegral_condKernel_univ_right, lintegral_abs_det_fderiv_eq_addHaar_image, addHaar_image_eq_zero_of_det_fderivWithin_eq_zero, ProbabilityTheory.condExpKernel_comp_trim, Measure.haarScalarFactor_smul, ProbabilityTheory.IsCondKernelCDF.integral, Measure.OuterRegular.smul_nnreal, mul_meas_ge_le_pow_eLpNorm', Real.smul_map_diagonal_volume_pi, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, Measure.map_fst_prod, ProbabilityTheory.Kernel.traj_map_updateFinset, exists_null_pairwise_disjoint_diff, Measure.addHaar_ball_of_pos, ProbabilityTheory.Kernel.swapRight_apply, ProbabilityTheory.Kernel.lintegral_fst, Measure.AbsolutelyContinuous.zero, Real.volume_val, volume_pi_pi, Measure.rnDeriv_restrict, lintegral_singleton, Measure.haarMeasure_self, ProbabilityTheory.Kernel.coeAddHom_apply, PMF.toMeasure_ofFintype_apply, Conservative.frequently_measure_inter_ne_zero, lintegral_countable, Measure.mkMetric_apply, ProbabilityTheory.Kernel.IsCondKernel.isProbabilityMeasure_ae, Measure.addHaar_eq_zero_of_disjoint_translates_aux, Measure.count_singleton', Measure.map_comp, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atTop, Measure.restrict_add_restrict_compl, IsProbabilityMeasure.neZero, Real.volume_pi_ball, Measure.const_comp, Measure.iInf_IicSnd_gt, biSup_measure_Iic, measurable_measure_add_right, Measure.sum_apply_of_countable, NumberField.mixedEmbedding.convexBodyLT_volume, measure_integral_le_pos, AEStronglyMeasurable.integral_condExpKernel, measure_pos_iff_nonempty_of_isAddLeftInvariant, Measure.snd_zero, withDensity_apply_eq_zero, condExpL1_measure_zero, Measure.addHaar_preimage_smul, measure_spanningSets_lt_top, ae_eq_zero_of_forall_setIntegral_eq_of_sigmaFinite, PMF.toMeasure_apply, laverage_eq', condLExp_add_left, withDensity_eq_zero_iff, PMF.toMeasure_ofMultiset_apply, Complex.volume_sum_rpow_le, ae_measure_preimage_mul_right_lt_top, enorm_ae_le_eLpNormEssSup, Measure.addHaar_sphere_of_ne_zero, ProbabilityTheory.Kernel.ae_compProd_iff, withDensity_zero, MeasurePreserving.measure_preimage_emb, NullMeasurableSet.compl_toMeasurable_compl_ae_eq, meas_eLpNormEssSup_lt, condExp_bilin_of_aestronglyMeasurable_right, MeasurableSet.exists_isCompact_isClosed_diff_lt, Lp.ae_eq_zero_of_forall_setIntegral_eq_zero', AEStronglyMeasurable.smul_measure, ProbabilityTheory.cond_apply_self, MemLp.meas_ge_lt_top, Ergodic.eq_smul_of_absolutelyContinuous, Measure.IsAddHaarMeasure.domSMul, Ioo_ae_eq_Icc, LocallyBoundedVariationOn.ae_differentiableAt, AEStronglyMeasurable.ae_integrable_condKernel_iff, AEFinStronglyMeasurable.ae_eq_zero_of_forall_setIntegral_eq_zero, isFiniteMeasure_iff, Measure.MutuallySingular.add_left, Measure.hausdorffMeasure_le_liminf_sum, measure_inter_add_diffβ, ProbabilityTheory.Kernel.swap_apply, MemLp.condExpL2_ae_eq_condExp, ProbabilityTheory.Kernel.measurable_densityProcess_countableFiltration_aux, ProbabilityTheory.Kernel.deterministic_prod_apply', Measure.aemeasurable_lintegral, essSup_ennreal_smul_measure, ProbabilityTheory.Kernel.coe_zero, measure_smul_eq_zero_iff, FiniteMeasure.restrict_apply_measure, tendsto_measure_biInter_gt, Measure.comap_preimage, Measure.pi_hyperplane, PreErgodic.ae_eq_const_of_ae_eq_comp, ae_eq_restrict_of_forall_setIntegral_eq, Measure.univ_pi_Ioo_ae_eq_Icc, measure_lt_one_eq_integral_div_gamma, div_ae_eq_one, ProbabilityTheory.cond_pos_of_inter_ne_zero, meas_le_ae_eq_meas_lt, Measure.forall_measure_inter_spanningSets_eq_zero, ProbabilityMeasure.measurable_fun_prod, Supermartingale.le_zero_of_predictable, Measure.toENNRealVectorMeasure_apply, SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensity, Measure.rnDeriv_eq_one_iff_eq, measure_neg_vadd_inter, ProbabilityTheory.Kernel.isIrreducible_iff, SimpleFunc.measure_preimage_lt_top_of_integrable, Measure.addHaarMeasure_closure_self, Measure.conv_add, SimpleFunc.restrict_lintegral, StieltjesFunction.measure_singleton, tendsto_measure_iUnion_atTop, ae_nonneg_of_forall_setIntegral_nonneg_of_sigmaFinite, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, Measure.support_mem_ae_of_isLindelof, Measure.setIntegral_condKernel, Measure.ae_sum_iff, Measure.instHaveLebesgueDecompositionZeroRight, SignedMeasure.eq_rnDeriv, Continuous.ae_eq_iff_eq, Measure.InnerRegular.smul, ProbabilityTheory.integral_stieltjesOfMeasurableRat, MeasurableSet.measure_eq_iSup_isCompact_of_ne_top, ProbabilityTheory.condExp_ae_eq_integral_condDistrib, ae_isMeasurablyGenerated, Measure.nullMeasurableSet_prod, Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, Measure.measurable_map, measurePreserving_finTwoArrow_vec, ProbabilityTheory.Kernel.map_apply', Measure.setLIntegral_rnDeriv, piContent_cylinder, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, Measure.map_apply, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, ApproximatesLinearOn.norm_fderiv_sub_le, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Measure.addHaar_ball_mul, MeasurableEquiv.comap_apply, Integrable.measure_ge_lt_top, ProbabilityTheory.Kernel.instNeZeroMeasureCoeSectROfProdMk, QuasiErgodic.smul_measure, Measure.InnerRegular.instSum, LipschitzOnWith.ae_differentiableWithinAt_of_mem_real, ProbabilityTheory.posterior_boolKernel_apply_true, isProbabilityMeasureSMul, measure_eq_top_of_subset_compl_sigmaFiniteSetWRT, IsCompact.exists_open_superset_measure_lt_top', VAddInvariantMeasure.add, Measure.measure_toMeasurable_inter, ProbabilityTheory.Kernel.parallelComp_apply_prod, Measure.add_right_inj, measure_lt_top, condExp_stopping_time_ae_eq_restrict_eq, indicatorConstLp_coeFn_mem, eventuallyConst_smul_set_ae, condExpL1_of_aestronglyMeasurable', map_mul_left_ae, IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div, IsFundamentalDomain.covolume_eq_volume, ProbabilityTheory.avgRisk_le_mul', ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, blimsup_thickening_mul_ae_eq_aux, IsFundamentalDomain.measure_le_of_pairwise_disjoint, Measure.OuterRegular.zero, ProbabilityTheory.Kernel.restrict_apply, Measure.add_comp, AEEqFun.coeFn_neg, lintegral_indicator_const_comp, ProbabilityTheory.Kernel.iIndepSet.meas_biInter, Monotone.ae_differentiableAt, Measure.comp_eq_sum_of_countable, ProbabilityTheory.iCondIndep_iff, measure_biUnion_toMeasurable, condExpL2_indicator_ae_eq_smul, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, Filtration.condExp_condExp, Measure.setIntegral_condKernel_univ_left, StronglyMeasurable.integral_kernel_prod_right, VitaliFamily.FineSubfamilyOn.measure_le_tsum, ae_eq_condLExp, Measure.haveLebesgueDecomposition_add, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Measure.prod_prod_le, Measure.sInf_caratheodory, LinearMap.exists_map_addHaar_eq_smul_addHaar, Integrable.measure_lt_lt_top, nndist_integral_add_measure_le_lintegral, ProbabilityTheory.Kernel.mutuallySingular_singularPart, curveIntegralFun_trans_aeeq_right, addEquivAddHaarChar_smul_preimage, Measure.measure_sub_singularPart, ProbabilityTheory.iIndepSets.meas_iInter, ProbabilityTheory.bayesRisk_eq_iInf_measure_of_subsingleton, AEMeasurable.add_measure, AEStronglyMeasurable.prodMk_right, ProbabilityTheory.stronglyMeasurable_integral_condDistrib, AEEqFun.coeFn_sub, Measure.sum_add_sum_compl, Measure.sum_fintype, Measure.pi_pi_aux, StieltjesFunction.measure_univ, integrableOn_const_iff, EuclideanSpace.volume_closedBall_fin_three, measure_inter_lt_top_of_right_ne_top, ProbabilityTheory.measurable_condDistrib, AEEqFun.coeFn_le, Measure.discard_comp, exists_isSigmaFiniteSet_measure_ge, map_add_left_ae, measure_preimage_vadd_of_nullMeasurableSet, essInf_measure_zero, NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero, measurable_measure_mul_right, ProbabilityTheory.covarianceOperator_zero, rnDeriv_conv, Real.volume_preimage_mul_left, IsAddFundamentalDomain.measure_eq, memLp_const_iff, Measure.restrict_eq_zero, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, Real.volume_pi_Ico, ae_add_measure_iff, Integrable.integral_norm_condDistrib_map, Measure.mkMetric_le_liminf_tsum, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, measure_mul_right_null, Measure.hausdorffMeasure_mono, Metric.measure_closedBall_pos_iff, ae_zero, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_forall_integrable_exp_mul, Lp.simpleFunc.sub_toSimpleFunc, volume_setOf_liouville, Measure.AbsolutelyContinuous.add_left_iff, Measure.rnDeriv_smul_left_of_ne_top, measure_sigmaFiniteSetGE_le, Measure.mem_cofinite, integral_eq_zero_iff_of_nonneg, condExp_smul_of_aestronglyMeasurable_right, NNReal.count_const_le_le_of_tsum_le, ProbabilityTheory.Kernel.fst_real_apply, Measure.toOuterMeasure_apply, ProbabilityTheory.setBernoulli_singleton, inv_ae, ProbabilityTheory.Kernel.piecewise_apply', Real.map_matrix_volume_pi_eq_smul_volume_pi, IsProjectiveMeasureFamily.measure_univ_eq_of_subset, union_ae_eq_left_iff_ae_subset, MulAction.aeconst_of_aestabilizer_eq_top, Measure.snd_compProd, memLp_measure_zero, Measure.AbsolutelyContinuous.comp_right, MeasurableSet.exists_isCompact_lt_add, Measure.restrict_apply_superset, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, sfiniteSeq_le, tendsto_measure_of_tendsto_indicator, SimpleFunc.const_lintegral_restrict, aestronglyMeasurable_zero_measure, ProbabilityTheory.Kernel.indepSet_iff_measure_inter_eq_mul, ProbabilityTheory.Kernel.compProd_deterministic_apply, AEEqFun.coeFn_comp, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_mem, tendstoInMeasure_iff_norm, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Content.measure_eq_content_of_regular, Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, Measure.count_apply_eq_top, ProbabilityTheory.Kernel.Invariant.def, SignedMeasure.singularPart_totalVariation, VitaliFamily.measure_limRatioMeas_zero, ProbabilityTheory.Kernel.rnDeriv_singularPart, ProbabilityTheory.Indep_iff, AEEqFun.toGerm_eq, ProbabilityTheory.condIndepSets_singleton_iff, BoundedVariationOn.ae_differentiableAt_of_mem_uIcc, Lp.simpleFunc.smul_toSimpleFunc, Real.volume_Icc_pi, Measure.singularPart_def, ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self, eLpNorm_indicator_sub_le_of_dist_bdd, Measure.infinitePi_pi, BoundedContinuousFunction.lintegral_nnnorm_le, addHaarScalarFactor_smul_eq_distribHaarChar, IsFoelner.tendsto_meas_smul_symmDiff, AEEqFun.coeFn_const, measure_mul_measure_eq, ae_differentiableAt_norm, ProbabilityTheory.indepSets_singleton_iff, Measure.rnDeriv_add_singularPart, addMeasure_map_restrict_apply, injective_dirac, Measure.instIsProbabilityMeasureBindCoeKernelOfIsMarkovKernel, eLpNorm'_measure_zero_of_pos, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, ProbabilityTheory.Kernel.compProd_eq_tsum_compProd, Measure.mutually_singular_measure_sub, VitaliFamily.ae_tendsto_lintegral_div, VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', Measure.smul_measure_isAddInvariant_le_of_isCompact_closure, AEFinStronglyMeasurable.ae_nonneg_of_forall_setIntegral_nonneg, ProbabilityTheory.Kernel.prodMkLeft_apply, IsometryEquiv.hausdorffMeasure_image, measure_inv_smul_sdiff, ProbabilityTheory.Kernel.lintegral_withDensity, ProbabilityTheory.Kernel.rnDeriv_eq_rnDeriv_measure, llr_tilted_right, measure_neg_null, pdf.uniformPDF_eq_pdf, condExp_mul_of_aestronglyMeasurable_right, Measure.comapβ_apply, measure_eq_zero_or_top_of_subset_compl_sigmaFiniteSet, StieltjesFunction.measure_Iic_of_tendsto_atBot_atBot, Measure.join_sum, Real.smul_map_volume_mul_left, sub_ae_eq_zero, ProbabilityTheory.Kernel.integrable_densityProcess, ProbabilityTheory.uniformOn_empty, eLpNorm_eq_zero_iff, ProbabilityTheory.Kernel.martingale_densityProcess, ProbabilityTheory.strong_law_ae, IsProjectiveMeasureFamily.congr_cylinder_of_subset, PreErgodic.measure_self_or_compl_eq_zero, IsClosed.measure_eq_one_iff_eq_univ, condExpIndSMul_empty, measure_vadd, prob_le_one, measure_union_lt_top_iff, lintegral_nnnorm_condExpL2_indicator_le, restrict_dirac, Measure.map_linearMap_addHaar_eq_smul_addHaar, Measure.coeAddHom_apply, Martingale.eq_zero_of_predictable, Measure.join_map_map, Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, AEFinStronglyMeasurable.ae_eq_of_forall_setIntegral_eq, lpNorm_smul_measure_of_ne_zero, Measure.integral_condKernel, aestronglyMeasurable_iff_aemeasurable_separable, Real.volume_singleton, Measure.restrict_apply, measure_lintegral_le_pos, Measure.ae_sum_eq, Measure.mutuallySingular_of_mutuallySingular_compProd, Integrable.norm_integral_condDistrib, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_pos_eq_zero_of_hasSubGaussianMGF_zero, BoxIntegral.Box.measure_coe_lt_top, ProbabilityTheory.iIndepFun.meas_biInter, map_sub_right_ae, StieltjesFunction.measure_univ_of_tendsto_atTop_atTop, AddCircle.add_projection_respects_measure, laverage_zero_measure, LipschitzWith.ae_lineDifferentiableAt, Measure.addHaarScalarFactor_smul_congr, ProbabilityTheory.uniformOn_eq_zero, ProbabilityTheory.condDistrib_ae_eq_iff_measure_eq_compProd, lintegral_abs_det_fderiv_le_addHaar_image_aux1, Measure.MeasureDense.fin_meas_approx, lintegral_le_iSup_mul, NullMeasurableSet.smul_measure, ProbabilityTheory.Kernel.boolKernel_apply, ae_eq_of_forall_setIntegral_eq_of_sigmaFinite, Integrable.measure_gt_lt_top, Measure.rnDeriv_mul_rnDeriv, ProbabilityTheory.stronglyMeasurable_condExpKernel, SignedMeasure.totalVariation_zero, ProbabilityTheory.setBernoulli_apply', Integrable.tendsto_ae_condExp, ProbabilityTheory.iIndepSets_iff, Measure.sum_comp_equiv, Measure.mutuallySingular_compProd_right_iff, exists_pos_measure_of_cover, blimsup_cthickening_ae_le_of_eventually_mul_le_aux, Real.volume_pi_Ioc, ProbabilityTheory.Kernel.ae_lt_top_of_comp_ne_top, Measure.instNeZeroOfNonempty, Martingale.stoppedValue_ae_eq_condExp_of_le_of_countable_range, aeconst_of_dense_setOf_preimage_smul_eq, ae_toFinite, Lp.ae_eq_zero_of_forall_setIntegral_eq_zero, BoxIntegral.Box.measure_Icc_lt_top, Measure.QuasiMeasurePreserving.smul_measure, AEEqFun.compMeasurable_toGerm, map_restrict_ae_le_map_indicator_ae, Real.volume_emetric_closedBall, ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure, mem_ae_dirac_iff, setLIntegral_nnnorm_condExpL2_indicator_le, Measure.rnDeriv_lt_top, lpNorm_measure_zero, ProbabilityTheory.Kernel.indepFun_iff_measure_inter_preimage_eq_mul, prob_compl_eq_one_subβ, ProbabilityTheory.Kernel.prod_apply, Besicovitch.ae_tendsto_rnDeriv, Ergodic.iff_mem_extremePoints_measure_univ_eq, Measure.mkMetric_top, Measure.addHaarMeasure_eq_iff, ProbabilityTheory.avgRisk_le_iSup_risk, ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd, pdf.IsUniform.measure_preimage, Measure.count_eq_zero_iff, ProbabilityTheory.condVar_smul, map_add_right_ae, prob_compl_eq_one_iff, ae_withDensity_iff_ae_restrict', Measure.restrict_biUnion_le, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, ProbabilityTheory.Kernel.setIntegral_const, Measure.zero_toOuterMeasure, instSFiniteHSMulENNRealMeasure, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_le, measure_univ_of_isMulLeftInvariant, ae_restrict_iUnion_eq, Real.volume_ball, Measure.addHaar_preimage_continuousLinearMap, Measure.ae_prod_iff_ae_ae, condExp_finset_sum, Real.volume_Icc_pi_toReal, Measure.mkMetric_mono, mulEquivHaarChar_smul_map, InformationTheory.klDiv_zero_right, AEEqFun.liftRel_mk_mk, Measure.map_div_left_ae, IsFoelner.eventually_meas_ne_top, Measure.restrict_inter_add_diffβ, Measure.prod_apply_le, ProbabilityTheory.Kernel.le_compProd_apply, ae_restrict_memβ, ProbabilityTheory.ofReal_condCDF_ae_eq, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, Measure.dirac_apply', Measure.countable_meas_pos_of_disjoint_iUnionβ, Measure.coe_toOuterMeasure, distribHaarChar_apply, volume_sum_rpow_lt, unitInterval.volume_uIcc, ZSpan.volume_fundamentalDomain, ProbabilityTheory.covarianceBilin_zero, condExp_neg, ProbabilityTheory.Kernel.fst_apply, MeasurePreserving.add_measure, condExp_mul_of_stronglyMeasurable_right, unitInterval.volume_Ici, measure_singleton_lt_top, Measure.setIntegral_compProd, SimpleFunc.restrict_const_lintegral, ProbabilityTheory.Kernel.deterministic_apply, ProbabilityTheory.Kernel.iIndepSets.meas_biInter, measure_pos_iff_nonempty_of_vaddInvariant, ZSpan.measure_fundamentalDomain, lintegral_abs_det_fderiv_le_addHaar_image, ProbabilityTheory.setLIntegral_condKernel, ProbabilityTheory.condExpKernel_ae_eq_condExp', hahn_decomposition, ae_withDensity_iff, isAddLeftInvariant_smul, ProbabilityTheory.lintegral_condKernel, Measure.eq_zero_of_absolutelyContinuous_of_mutuallySingular, ProbabilityMeasure.eq_of_forall_toMeasure_apply_eq_iff, FiniteMeasure.eq_of_forall_toMeasure_apply_eq_iff, Integrable.condKernel_ae, Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, ProbabilityTheory.condDistrib_comp_map, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup, ProbabilityTheory.aestronglyMeasurable_integral_condDistrib, Measure.sub_le_iff_le_add, Measure.addHaar_ball_center, Measure.ae_eq_or_eq_iff_map_eq_dirac_add_dirac, measureReal_zero, measure_isClosed_eq_of_forall_lintegral_eq_of_isFiniteMeasure, MeasurableSet.exists_isCompact_diff_lt, lintegral_eq_zero_iff', ae_restrict_eq_bot, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_map_map, tendstoInMeasure_iff_dist, Measure.measure_toMeasurable_inter_of_sFinite, Measure.toSphere_apply_univ, MeasurableSet.measure_eq_iSup_isCompact, Lp.coeFn_compMeasurePreserving, measure_symmDiff_le, unitInterval.volume_uIoo, laverage_eq, ae_eq_zero_restrict_of_forall_setIntegral_eq_zero, MeasurableEmbedding.rnDeriv_map_aux, Measure.Regular.smul, Measure.hausdorffMeasure_smulβ, ae_ae_add_linearMap_mem_iff, eLpNorm_one_smul_measure, Measure.withDensity_rnDeriv_le, ProbabilityTheory.HasLaw.ae_iff, Monotone.ae_hasDerivAt, condExp_bilin_of_aestronglyMeasurable_left, ProbabilityTheory.IsCondKernelCDF.setIntegral, ProbabilityTheory.Kernel.withDensity_absolutelyContinuous, RealRMK.rieszMeasure_le_of_eq_one, condExp_condExp_of_le, EuclideanSpace.volume_closedBall_fin_two, Measure.setIntegral_condKernel_univ_right, enorm_indicatorConstLp_le, AEEqFun.coeFn_abs, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, exists_spanning_measurableSet_le, ProbabilityTheory.condExp_ae_eq_trim_integral_condExpKernel_of_stronglyMeasurable, essSup_eq_sInf, Real.volume_pi_Ioc_toReal, FiniteMeasure.coeFn_def, addHaar_image_le_lintegral_abs_det_fderiv_aux1, JordanDecomposition.zero_posPart, tendsto_measure_cthickening, ProbabilityTheory.Kernel.ae_kernel_lt_top, vadd_set_ae_le, Measure.absolutelyContinuous_comp_of_countable, VitaliFamily.ae_tendsto_limRatio, measure_sdiff_neg_vadd, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, ProbabilityTheory.condExp_ae_eq_trim_integral_condExpKernel, MeasurePreserving.smul_measure, measure_compl_le_add_iff, IsOpen.measure_pos, Measure.map_def, Measure.condKernel_apply_of_ne_zero, Set.exists_isOpen_lt_add, withDensity_apply_eq_zero', ProbabilityTheory.Kernel.copy_apply, ProbabilityTheory.Kernel.rnDeriv_ne_top, condExp_ofNat, tendsto_measure_Icc, zero_trim, SimpleFunc.lintegral_restrict, Measure.nonpos_iff_eq_zero', measure_union_add_inter, BoxIntegral.Box.coe_ae_eq_Icc, Measure.prod_apply, measure_laverage_le_pos, Lp.coeFn_smul, StieltjesFunction.measurable_measure, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, Measure.MutuallySingular.smul, Real.volume_Iio, Measure.InnerRegularWRT.of_sigmaFinite, UnitAddCircle.measure_univ, ProbabilityTheory.Kernel.parallelComp_def, InformationTheory.klDiv_zero_left, measure_biUnion_eq_iSup, PreErgodic.smul_measure, measure_neg_vadd_symmDiff, AEEqFun.coeFn_compQuasiMeasurePreserving, SMul.sigmaFinite, Measure.addHaarMeasure_unique, ProbabilityTheory.IsAEKolmogorovProcess.ae_eq_mk, AEMeasurable.ae_inf_principal_eq_mk, limsup_measure_closed_le_iff_liminf_measure_open_ge, Measure.compProd_apply_univ, ae_restrict_of_forall_mem, isMulLeftInvariant_smul, eventually_mul_left_iff, Set.Countable.ae_notMem, Measure.pi_ball, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup, condExp_stronglyMeasurable_simpleFunc_mul, ProbabilityTheory.covarianceBilinDual_zero, measureUnivNNReal_eq_zero, ProbabilityTheory.IsRatCondKernelCDFAux.mono, Measure.isMulLeftInvariant_eq_smul_of_innerRegular, Measure.le_iff', ProbabilityTheory.Kernel.iIndepFun_zero_right, MeasurableSet.exists_isClosed_lt_add, FiniteMeasure.toMeasure_mk, Besicovitch.exist_finset_disjoint_balls_large_measure, Measure.mem_support_iff, measure_le_measure_union_left, Measure.ae_prod_mem_iff_ae_ae_mem, Measure.map_sub_left_ae, RealRMK.measure_le_of_isCompact_of_integral, blimsup_cthickening_ae_le_of_eventually_mul_le, BoxIntegral.Box.Ioo_ae_eq_Icc, PMF.toMeasure_apply_eq_toOuterMeasure_apply, ProbabilityTheory.Kernel.setIntegral_deterministic, Measure.restrict_union, Measure.compProd_apply, IsProjectiveLimit.measure_univ_eq, ProbabilityTheory.Kernel.eq_boolKernel, Filter.Eventually.volume_pos_of_nhds_real, Measure.lintegral_rnDeriv_le, AEDisjoint.diff_ae_eq_right, Lp.coeFn_le, ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf', ProbabilityTheory.condIndepSet_iff, lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, Lp.simpleFunc.add_toSimpleFunc, ae_le_toMeasurable, ProbabilityTheory.Kernel.setLIntegral_restrict, Measure.restrict_union', ProbabilityTheory.Kernel.partialTraj_compProd_traj, instSFiniteOfNatMeasure, ProbabilityTheory.Kernel.lintegral_prodMkRight, ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map, IntegrableOn.add_measure, UnitAddTorus.coeFn_mFourierLp, Integrable.integral_norm_condExpKernel, StronglyMeasurable.integral_kernel_prod_right', Measure.restrict_mono_set, PMF.toOuterMeasure_apply_le_toMeasure_apply, isFiniteMeasureSMulOfNNRealTower, Ioi_ae_eq_Ici, ProbabilityTheory.IsZeroOrMarkovKernel.isZeroOrProbabilityMeasure, Measure.sum_apply, Measure.ext_prodβ_iff', ae_eq_of_forall_setLIntegral_eq_of_sigmaFinite, Measure.add_comp', ProbabilityTheory.IsCondKernelCDF.setLIntegral, measure_le_laverage_pos, ProbabilityTheory.Kernel.condKernelCountable_apply, Measure.lt_iff', AEEqFun.ext_iff, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, Measure.rnDeriv_smul_left', lpMeasToLpTrimLie_symm_indicator, FiniteMeasure.toMeasure_add, ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero', condExp_mul_of_aestronglyMeasurable_left, projectiveFamilyContent_cylinder, IsAddFundamentalDomain.measure_set_eq, Antitone.measure_iUnion, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', ProbabilityTheory.Kernel.finset_sum_apply', StronglyMeasurable.integral_condExpKernel, ae_nonneg_restrict_of_forall_setIntegral_nonneg, ProbabilityTheory.Kernel.lintegral_map, ProbabilityTheory.Kernel.pow_add_apply_eq_lintegral, measure_le_lintegral_pos, volume_sum_rpow_le, Measure.pi_map_eval, ProbabilityTheory.IsMarkovKernel.isProbabilityMeasure, ProbabilityTheory.ae_cond_mem, ProbabilityMeasure.coeFn_def, instNonemptySubtypeMeasureIsProbabilityMeasure, ExistsSeqTendstoAe.seqTendstoAeSeq_spec, eventually_sub_right_iff, SimpleFunc.map_lintegral, ProbabilityTheory.avgRisk_zero_prior, Measure.map_eq_zero_iff, Measure.notMem_support_iff, isMulRightInvariant_smul, measure_le_setAverage_pos, SMulInvariantMeasure.zero, Measure.singularPart_le, ae_map_iff, Lp.coeFn_negPart_eq_max, Ico_ae_eq_Ioc, Real.volume_Ico, IsFundamentalDomain.iUnion_smul_ae_eq, ProbabilityTheory.mgf_add_measure, ae_measure_preimage_mul_right_lt_top_of_ne_zero, SimpleFunc.memLp_iff, ProbabilityTheory.Kernel.aemeasurable, ProbabilityTheory.IndepSet_iff, IsProbabilityMeasure.measure_univ, ProbabilityTheory.Kernel.condKernel_apply_eq_condKernel, eLpNorm'_smul_measure, Measure.restrict_apply_eq_zero, VitaliFamily.ae_tendsto_average_norm_sub, ae_neBot, eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, OrthonormalBasis.volume_parallelepiped, Lp.ae_eq_of_forall_setIntegral_eq', eLpNorm_smul_measure_of_ne_top, ae_eq_trim_iff_of_aestronglyMeasurable, laverage_mul_measure_univ, ProbabilityTheory.Kernel.meas_countablePartitionSet_le_of_fst_le, AddCircle.volume_closedBall, tendsto_measure_vadd_diff_isCompact_isClosed, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, NumberField.mixedEmbedding.realSpace.volume_eq_zero, Measure.MeasureDense.indicatorConstLp_subset_closure, Measure.isMulLeftInvariant_eq_smul_of_regular, ProbabilityTheory.preCDF_le_one, Measure.pi_Ico_ae_eq_pi_Icc, Measure.smul_toOuterMeasure, memLp_const_iff_enorm, FinMeasAdditive.smul_measure_iff, ProbabilityTheory.Kernel.discard_apply, Martingale.condExp_stoppedValue_stopping_time_ae_eq_restrict_le, Measure.map_eq_sum, tendsto_smul_ae, Measure.restrict.neZero, AEMeasurable.ae_of_join, ProbabilityTheory.IsSFiniteKernel.sFinite, tendsto_measure_Iic_atTop, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, ProbabilityTheory.centralMoment_zero_measure, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, Measure.countable_meas_level_set_pos, Measurable.lintegral_kernel_prod_right'', ProbabilityTheory.Kernel.id_prod_apply', IsProjectiveMeasureFamily.eq_zero_of_isEmpty, Measure.rnDeriv_smul_right_of_ne_top', Measure.pi_singleton, ProbabilityTheory.Kernel.condDistrib_trajMeasure, ae_eq_zero_of_integral_contDiff_smul_eq_zero, unitInterval.volume_Icc, tsum_measure_le_measure_univ, tendsto_measure_of_tendsto_indicator_of_isFiniteMeasure, Martingale.eq_zero_of_predictable', ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, projectiveFamilyContent_congr, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_apply_eq_zero, measure_add_diff, ProbabilityTheory.variance_zero_measure, IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul, Measure.everywherePosSubset_ae_eq, Measure.singularPart_zero_right, volume_regionBetween_eq_lintegral', Integrable.norm_integral_condKernel, condExp_stronglyMeasurable_simpleFunc_bilin, piContent_eq_measure_pi, Measure.restrict_iUnion_apply, DomMulAct.smul_aeeqFun_aeeq, Measure.restrict_apply_le, exists_null_frontier_thickening, InnerProductSpace.volume_ball, JordanDecomposition.exists_compl_positive_negative, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, integral_finset_sum_measure, ProbabilityTheory.Kernel.ae_comp_iff, Measure.bind_apply_le, forall_measure_preimage_mul_iff, Measure.restrict_union_add_inter, Supermartingale.le_zero_of_predictable', piecewise_ae_eq_restrict_compl, withDensity_add_left, Measure.eventually_cofinite, ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_le, ProbabilityTheory.posterior_prod_id_comp, condExp_indicator, HasOuterApproxClosed.measure_le_lintegral, setLIntegral_eq_zero_iff, isProbabilityMeasure_ite, VectorMeasure.ennrealToMeasure_apply, measure_lt_top_of_isCompact_of_isMulLeftInvariant, integrable_smul_measure, ProbabilityTheory.IndepFun.pdf_mul_eq_mlconvolution_pdf, ProbabilityTheory.bayesRisk_const_of_nonempty, SMulInvariantMeasure.add, Measure.add_apply, setLAverage_eq', dirac_eq_zero_iff_not_mem, eLpNorm_le_add_measure_left, Measure.rnDeriv_add, ProbabilityTheory.Kernel.instIsIrreducibleHSMulENNRealMeasure, Measure.withDensity_rnDeriv_eq_zero, Ioo_ae_eq_Ico, ergodicSMul_iff, SchwartzMap.coeFn_toLp, ProbabilityTheory.cond_inter_self, lintegral_deriv_eq_volume_image_of_antitoneOn, nullMeasurableSet_smul_measure_iff, uniformIntegrable_zero_meas, aeconst_of_dense_aestabilizer_vadd, Measure.count_apply_lt_top, Measure.restrict_apply_univ, IsTightMeasureSet.inter, Measure.compProd_id_eq_copy_comp, Measure.finset_sum_apply, Measure.add_sub_cancel, AEEqFun.coeFn_mk, MeasurableEmbedding.map_injective, Measure.infinitePiNat_map_piCongrLeft, ProbabilityTheory.iCondIndepSets_singleton_iff, Ioc_ae_eq_Icc, Measure.MutuallySingular.restrict_nullSet, measure_iInter_eq_iInf_measure_iInter_le, ProbabilityTheory.mgf_zero_measure, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_measure_eq_zero, UnifIntegrable.unifIntegrable_of_ae_tendsto, Measure.toSignedMeasure_smul, ProbabilityTheory.tilted_mul_apply_mgf', ProbabilityTheory.uniformOn_empty_meas, addHaar_image_le_lintegral_abs_det_fderiv_aux2, ProbabilityTheory.Kernel.setLIntegral_deterministic, ProbabilityTheory.ae_cond_memβ, Integrable.ae_eq_zero_of_forall_setIntegral_eq_zero, PreErgodic.ae_empty_or_univ, Measure.mapβ_mk_apply_of_aemeasurable, tendsto_measure_iInter_le, tendsto_measure_thickening, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, ProbabilityTheory.bayesRisk_le_mul', Measure.comap_apply, Measure.addHaar_parallelepiped, lintegral_indicator_const_le, ProbabilityTheory.Kernel.ae_eq_of_compProd_eq, ProbabilityTheory.inter_pos_of_cond_ne_zero, smulInvariantMeasure_iff, Measure.setLIntegral_rnDeriv', ProbabilityTheory.iIndepSet.meas_biInter, ProbabilityTheory.uniformOn_eq_zero_iff, ProbabilityTheory.Kernel.measurable_kernel_prodMk_left', SimpleFunc.lintegral_eq_of_subset', IsAddFundamentalDomain.iUnion_vadd_ae_eq, tendsto_measure_norm_gt_of_isTightMeasureSet, hausdorffMeasure_lineMap_image, Measure.lintegral_condKernel, aeconst_of_dense_setOf_preimage_vadd_eq, Measure.sum_cond, intervalIntegral.integral_smul_measure, Measure.pi_univ, FiniteMeasure.limsup_measure_closed_le_of_tendsto, dirac_eq_one_iff_mem, le_measure_symmDiff, ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf, ProbabilityTheory.Kernel.measurable_trajFun, ae_restrict_neBot, Measure.restrict_congr_meas, ProbabilityTheory.Kernel.partialTraj_map_frestrictLeβ_apply, Measure.pi_Ioi_ae_eq_pi_Ici, measure_compl_sigmaFiniteSet_eq_zero_iff_sigmaFinite, ae_eq_restrict_biUnion_finset_iff, Set.OrdConnected.null_frontier, Measure.sum_applyβ, restrict_compl_sigmaFiniteSet_eq_zero_or_top, eLpNorm_le_add_measure_right, ProbabilityTheory.gaussianReal_apply, ProbabilityTheory.Kernel.densityProcess_fst_univ_ae, Measure.addHaarMeasure_apply, Measure.zero_prod, Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable, Measure.prod_prod, tilted_apply_eq_ofReal_integral, measure_lt_top_of_subset, ae_eq_zero_of_integral_smooth_smul_eq_zero, Measure.MeasureDense.fin_meas, ProbabilityTheory.setLIntegral_condKernel_univ_left, ProbabilityMeasure.le_liminf_measure_open_of_tendsto, StieltjesFunction.measure_Ici, ProbabilityTheory.condExp_set_generateFrom_singleton, ProbabilityTheory.cond_eq_inv_mul_cond_mul, ProbabilityTheory.Kernel.boolKernel_false, Measure.zero_conv, ae_dirac_iff, MemLp.smul_measure, ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zero_of_const_eq_zero, measure_iUnionβ, ProbabilityTheory.Kernel.lintegral_traj, measure_symmDiff_inv_smul, measure_vadd_eq_zero_iff, MeasurableSet.exists_isOpen_diff_lt, Integrable.integral_condExpKernel, Measure.WeaklyRegular.innerRegular_measurable, Real.volume_pi_le_prod_diam, meas_ge_le_lintegral_div, Measure.mutuallySingular_iff_disjoint, Lp.coeFn_sup, ProbabilityTheory.Kernel.setLIntegral_compProd_univ_left, ProbabilityTheory.Kernel.measurable_lintegral_indicator_const, Measure.ae_eq_or_eq_iff_eq_dirac_add_dirac, ProbabilityTheory.Kernel.comp_apply, pdf.IsUniform.pdf_toReal_ae_eq, Measure.parallelComp_comp_compProd, Measure.conv_smul_left, Integrable.add_measure, Set.Finite.measure_zero, ProbabilityTheory.condExp_generateFrom_singleton, Measure.measure_isAddHaarMeasure_eq_smul_of_isOpen, Measure.measure_eq_zero_of_subset_diff_everywherePosSubset, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', ProbabilityTheory.condDistrib_comp, ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet, AEEqFun.liftRel_iff_coeFn, condExp_smul, integrable_prod_iff, Measurable.setLIntegral_kernel_prod_left, Measure.isOpenPosMeasure_smul, Measure.coe_add, ProbabilityTheory.meas_ge_le_variance_div_sq, lintegral_indicator_oneβ, ae_eq_restrict_biUnion_iff, Measure.count_singleton, Martingale.stoppedValue_min_ae_eq_condExp, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel, Submartingale.zero_le_of_predictable, setAverage_eq', Measure.Regular.domSMul, Measure.bind_zero_right, IsAddFoelner.eventually_meas_ne_zero, Measure.AbsolutelyContinuous.add_right, measure_sigmaFiniteSetWRT', Measure.rnDeriv_add_right_of_mutuallySingular', VectorMeasure.equivMeasure_symm_apply, Measure.comp_eq_comp_const_apply, InnerProductSpace.volume_ball_of_dim_odd, Measure.univ_pi_Ico_ae_eq_Icc, Ergodic.smul_measure, StronglyMeasurable.exists_spanning_measurableSet_norm_le, ProbabilityTheory.Kernel.comp_discard', ProbabilityTheory.monotone_preCDF, ProbabilityTheory.Kernel.integral_const, Measure.rnDeriv_ne_top, IsCompact.measure_eq_iInf_isOpen, ProbabilityTheory.Kernel.add_apply, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, measure_add_measure_compl, Measure.addHaarMeasure_self, measure_inter_inv_smul, FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure, ProbabilityTheory.Kernel.HasSubgaussianMGF.isFiniteMeasure, measure_unionβ_aux, measure_le_lintegral_thickenedIndicator, Measure.ae_smul_measure_iff, BoxIntegral.Box.volume_apply', ProbabilityTheory.Kernel.compProd_eq_zero_iff, Real.disjoint_residual_ae, Measure.ae_completion, Integrable.ae_eq_of_withDensityα΅₯_eq, SimpleFunc.FinMeasSupp.meas_preimage_singleton_ne_zero, Measure.instSMulCommClassDomMulActNNReal, ProbabilityTheory.Kernel.ext_iff, measure_inter_lt_top_of_left_ne_top, Measure.pi_Ioo_ae_eq_pi_Icc, weightedSMul_add_measure, measure_neg_vadd_sdiff, ProbabilityTheory.Kernel.piecewise_apply, ProbabilityTheory.Kernel.lintegral_compProd', eLpNormEssSup_smul_measure, ProbabilityTheory.Kernel.indepSet_zero_right, ae_restrict_union_iff, mem_map_restrict_ae_iff, TendstoInMeasure.exists_seq_tendsto_ae, AEEqFun.smul_toGerm, comap_subtype_coe_apply, withDensity_eq_iff, ProbabilityTheory.condKernel_compProd, dimH_eq_iInf, tendsto_measure_Icc_nhdsWithin_right, ProbabilityTheory.Kernel.HasSubgaussianMGF.mgf_le, Measure.sInf_apply, ProbabilityTheory.Kernel.prodMkRight_apply, Measure.fst_apply, Measure.singularPart_withDensity, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, smul_ae, integrable_conv_iff, Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure, Measurable.setLIntegral_kernel, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, Integrable.to_average, Measure.inv_rnDeriv, ProbabilityTheory.IsRatCondKernelCDFAux.mono', Set.Countable.measure_zero, measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero, AEEqFun.coeFn_sup, ae_restrict_iffβ, ProbabilityTheory.strong_law_aux6, measure_isOpen_pos_of_vaddInvariant_of_ne_zero, tendsto_sum_indicator_atTop_iff', ProbabilityTheory.Kernel.rnDerivAux_le_one, ProbabilityTheory.Kernel.comp_const, IsOpen.measure_eq_iSup_isCompact, lintegral_countable', tilted_const', SimpleFunc.integrable_iff, ae_bdd_liminf_atTop_rpow_of_eLpNorm_bdd, limsup_trim, Measure.fst_univ, Monotone.measure_iInter, ae_le_eLpNormEssSup, tendsto_measure_Ioc_atBot, Measure.univ_pi_Ioi_ae_eq_Ici, Measure.inf_apply, Measurable.lintegral_kernel, Measure.jordanDecompositionOfToSignedMeasureSub_negPart, tilted_apply, measurable_measure_prodMk_left_finite, Measurable.lintegral_kernel_prod_left, Integrable.integral_condDistrib_map, Measure.infinitePi_singleton_of_fintype, SMulInvariantMeasure.measure_preimage_smul, toOuterMeasure_eq_inducedOuterMeasure, Measure.HaveLebesgueDecomposition.lebesgue_decomposition, smul_le_stoppedValue_hitting, FiniteMeasure.toMeasure_injective, PMF.toMeasure_uniformOfFintype_apply, Measure.integrable_compProd_iff, ProbabilityTheory.IsKolmogorovProcess.edist_eq_zero_of_const_eq_zero, MeasurePreserving.measure_preimage_equiv, ProbabilityTheory.Kernel.continuous_integral_integral, Measure.isMulInvariant_eq_smul_of_compactSpace, Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Integrable.condDistrib_ae, measure_eq_div_smul, AntilipschitzWith.le_hausdorffMeasure_image, Real.volume_Iic, SimpleFunc.lintegral_zero, rnDeriv_mconv, ProbabilityTheory.condIndepSets_iff, Measure.hausdorffMeasure_zero_or_top, ProbabilityTheory.Kernel.measurableSet_mutuallySingular, ProbabilityTheory.setLIntegral_toKernel_univ, IsOpen.ae_eq_empty_iff_eq, log_rnDeriv_tilted_left_self, ProbabilityTheory.iCondIndepSet_iff, AEEqFun.coeFn_compβMeasurable, ProbabilityTheory.uniformOn_eq_one_of, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, eLpNorm_indicator_const_le, condExp_add, ProbabilityTheory.condExpKernel_singleton_ae_eq_cond, isFoelner_iff, Measure.measure_toMeasurable_inter_of_cover, prob_compl_eq_zero_iff, exists_pos_ball, measure_union_add_interβ', mem_ae_iff_prob_eq_one, ae_eq_dirac', Measure.MutuallySingular.zero_left, ProbabilityTheory.Kernel.iIndepFun.measure_inter_preimage_eq_mul, measure_mul_laverage, condExp_ae_eq_condExpL1, sum_measure_preimage_singleton, Measure.toSphere_apply', Measure.comap_applyβ, Measure.add_mconv, ae_eq_univ_iff_measure_eq, Measure.volume_subtype_coe_le_volume, Real.volume_Icc, ProbabilityTheory.Kernel.lintegral_prod, ProbabilityTheory.condVar_ae_le_condExp_sq, ProbabilityTheory.IdentDistrib.measure_preimage_eq, Measure.compl_support_eq_sUnion, StronglyMeasurable.integral_condExpKernel', ProbabilityTheory.condDistrib_snd_prod, IsFoelner.tendsto_meas_smul_symmDiff_smul, Measure.smul_absolutelyContinuous, AEEqFun.pow_toGerm, FiniteMeasure.val_eq_toMeasure, ae_eq_bot, isTightMeasureSet_singleton, ProbabilityTheory.Kernel.setIntegral_densityProcess, JordanDecomposition.zero_negPart, DomAddAct.vadd_aeeqFun_aeeq, ae_nonneg_restrict_of_forall_setIntegral_nonneg_inter, vadd_mem_ae, ae_restrict_iff_subtype, ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, JordanDecomposition.smul_posPart, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel', ProbabilityTheory.IndepFun.meas_inter, measure_le_measure_closure_of_levyProkhorovEDist_eq_zero, StronglyMeasurable.integral_condDistrib, boundedBy_measure, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, tsum_meas_le_meas_iUnion_of_disjoint, AEEqFun.toGermMonoidHom_apply, ProbabilityTheory.Kernel.ext_iff', Measure.setLIntegral_condKernel, StieltjesFunction.measure_Ioi, Measure.coe_smul, Measure.le_liftLinear_apply, IsometryEquiv.hausdorffMeasure_preimage, Measure.compProd_eq_comp_prod, Integrable.ae_eq_of_forall_setIntegral_eq, DomAddAct.vadd_Lp_ae_eq, Lp.ae_tendsto_of_cauchy_eLpNorm', measure_iUnion, AddAction.coe_aestabilizer, AEDisjoint.eq, measure_complβ, FiniteMeasure.prod_apply, rnDeriv_mconv', Measure.smul_finite, ProbabilityTheory.Kernel.integral_densityProcess, Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure, MeasurableEmbedding.gaussianReal_comap_apply, Measure.finiteAt_principal, Measure.sum_apply_eq_zero, Module.Basis.addHaar_eq_iff, Lp.simpleFunc.neg_toSimpleFunc, SimpleFunc.lintegral_smul, Complex.volume_sum_rpow_lt, ProbabilityTheory.Kernel.IndepFun.meas_inter, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', VitaliFamily.ae_tendsto_div, exists_measure_pos_of_not_measure_iUnion_null, VitaliFamily.ae_tendsto_measure_inter_div, Measure.toSignedMeasure_add, measure_preimage_snd_singleton_eq_sum, SimpleFunc.const_lintegral, measure_lintegral_div_measure, ae_le_lpNorm_exponent_top, StronglyMeasurable.ae_le_trim_iff, Measure.IicSnd_apply, tendsto_measure_symmDiff_preimage_nhds_zero, condExp_ae_eq_condExpL1CLM, Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePos, Measure.measure_compl_support, Measure.restrict_unionβ, ProbabilityTheory.iIndepSets.meas_biInter, BoundedContinuousFunction.coeFn_toLp, ProbabilityTheory.Kernel.isProjectiveLimit_trajFun, ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd_of_measurable, map_eq_setLIntegral_pdf, Measure.sum_add_sum, Measure.singularPart_self, Measure.nnreal_smul_coe_apply, ProbabilityTheory.lintegral_toKernel_mem, ProbabilityTheory.Kernel.coe_finset_sum, indicatorConstLp_inj, ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self, Real.volume_pi_Ioo, LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem, ProbabilityTheory.Kernel.measurableSet_absolutelyContinuous, Measure.addHaar_image_linearMap, measure_univ_of_isAddLeftInvariant, Measure.ae_ennreal_smul_measure_iff, tendsto_ae_condExp, eLpNorm_const', Measure.everywherePosSubset_ae_eq_of_measure_ne_top, measure_lt_top_of_isCompact_of_isAddLeftInvariant, Measure.toENNRealVectorMeasure_add, IsTightMeasureSet.map, ProbabilityTheory.cond_iInter, ProbabilityTheory.Kernel.parallelComp_apply', ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, IsHahnDecomposition.ge_on_compl, levyProkhorovEDist_le_max_measure_univ, ProbabilityTheory.uniformOn_self, ae_restrict_le, AEStronglyMeasurable.ae_eq_mk, Measure.add_top, IsOpen.measure_eq_biSup_integral_continuous, ae_finsetSum_measure_iff, measure_map_restrict_apply, Measure.addHaarScalarFactor_smul_smul, Measure.mem_support_iff_forall, JordanDecomposition.real_smul_posPart_nonneg, AEEqFun.one_toGerm, isTightMeasureSet_of_isCompact_closure, integrableOn_add_measure, IsFiniteMeasure.average, Measure.rnDeriv_eq_zero_of_mutuallySingular, measure_union_eq_top_iff, Measure.restrict_iUnion_apply_eq_iSup, Measure.FiniteSpanningSetsIn.finite, hausdorffMeasure_homothety_image, Measure.absolutelyContinuous_smul, Measure.tendsto_ae_map, Measure.join_dirac, Measure.fst_add, Measure.mutuallySingular_iff_disjoint_ae, lintegral_nnnorm_condExpL2_indicator_le_real, ProbabilityTheory.Kernel.setLIntegral_density, integral_pos_iff_support_of_nonneg, count_withDensity, Measure.ae_comp_iff, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, setLIntegral_one, rnDeriv_ae_eq_condExp, withDensity_applyβ, VitaliFamily.ae_eventually_measure_zero_of_singular, toFinite_eq_zero_iff, Besicovitch.ae_tendsto_measure_inter_div, ergodicVAdd_iff, NoAtoms.measure_singleton, ProbabilityTheory.Kernel.lintegral_snd, ProbabilityTheory.Kernel.integrable_density, Measure.join_eq_bind, Measure.one_le_hausdorffMeasure_zero_of_nonempty, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Real.volume_pi_Ioo_toReal, Measure.rnDeriv_pos, Measure.coe_finset_sum, Measure.smul_measure_isMulInvariant_le_of_isCompact_closure, ProbabilityTheory.Kernel.lintegral_const, ProbabilityTheory.Kernel.instNeZeroMeasureCoeSectLOfProdMk, ProbabilityTheory.cond_add_cond_compl_eq, measure_diff_add_inter, ae_restrict_biUnion_finset_iff, Measure.restrict_zero, pdf.IsUniform.pdf_eq, Measure.bind_smul, Integrable.measure_norm_gt_lt_top, FiniteMeasure.toMeasure_normalize_eq_of_nonzero, Measure.lintegral_condKernel_mem, Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePos, measure_toMeasurable, IsFiniteMeasureOnCompacts.smul_nnreal, ProbabilityTheory.Kernel.setLIntegral_deterministic', sub_nonneg_ae, Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top, Integrable.ae_convolution_exists, AEStronglyMeasurable.ae_of_compProd, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, L1.SimpleFunc.negPart_toSimpleFunc, Measure.count_apply_finset', Measure.exists_sum_smul_dirac, ae_le_of_forall_setLIntegral_le_of_sigmaFiniteβ, Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet, condExp_stopping_time_ae_eq_restrict_eq_of_countable, Measure.MutuallySingular.zero_right, Integrable.norm_integral_condDistrib_map, ProbabilityTheory.condExpKernel_ae_eq_condExp, one_le_prob_iff, LipschitzWith.ae_differentiableAt, VitaliFamily.ae_tendsto_lintegral_div', Measure.toOuterMeasure_injective, Measure.MutuallySingular.measure_nullSet, ProbabilityTheory.Kernel.lintegral_prod_symm, ProbabilityTheory.IndepFun.pdf_mul_eq_mlconvolution_pdf', ProbabilityTheory.hasFiniteIntegral_comp_iff, hausdorffMeasure_vadd, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, measureReal_ennreal_smul_apply, ProbabilityTheory.aestronglyMeasurable_trim_condExpKernel, Measure.InnerRegularCompactLTTop.innerRegular, AEEqFun.coeFn_compMeasurable, ProbabilityTheory.IsFiniteKernel.isFiniteMeasure, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, Measure.deterministic_comp_eq_map, ProbabilityTheory.Kernel.indepSets_zero_right, Measure.pi_Ioo_ae_eq_pi_Ioc, union_ae_eq_right_iff_ae_subset, condExp_stopping_time_ae_eq_restrict_eq_of_countable_range, ProbabilityTheory.measurableSet_integrable, essSup_measure_zero, Measure.InnerRegularWRT.smul, Measure.addHaar_affineSubspace, Lp.simpleFunc.coeFn_le, measure_Icc_lt_top, pdf.indepFun_iff_pdf_prod_eq_pdf_mul_pdf, Real.volume_Ioc, ProbabilityTheory.Kernel.integral_density, Measure.dirac_apply_ne_zero_iff_eq_one, Metric.measure_closedEBall_pos, ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_mutuallySingularSetSlice, IsFundamentalDomain.measure_eq_tsum_of_ac, Measure.join_map_dirac, ProbabilityTheory.IndepFun.measure_inter_preimage_eq_mul, Measure.comap_smul, condLExp_smul_le, Measure.instSMulCommClassNNRealDomMulAct, tendsto_measure_sigmaFiniteSetGE, EuclideanSpace.volume_ball_fin_three, SignedMeasure.toMeasureOfLEZero_apply, Measure.integral_compProd, Convex.addHaar_frontier, Measure.QuasiMeasurePreserving.ae_map_le, AddSubgroup.index_mul_measure, ProbabilityTheory.Kernel.compProd_apply_univ_le, intervalIntegrable_const_iff, Martingale.condExp_stopping_time_ae_eq_restrict_eq_const_of_le_const, Measure.addHaar_image_continuousLinearEquiv, Measure.hausdorffMeasure_le_liminf_tsum, setLAverage_eq, Measure.le_map_apply, Lp.ae_tendsto_of_cauchy_eLpNorm, lintegral_zero_measure, condExp_of_aestronglyMeasurable', ProbabilityTheory.Kernel.lintegral_density, Integrable.integral_norm_condDistrib, isClosed_setOf_preimage_ae_eq, Measure.notMem_support_iff_exists, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Lp.simpleFunc.toSimpleFunc_toLp, measure_pos_iff_nonempty_of_smulInvariant, lintegral_finset, Complex.volume_closedBall, ProbabilityTheory.IsCondKernelCDF.integrable, Measure.rnDeriv_def, Lp.coeFn_nonneg, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, Measure.ae_le_iff_absolutelyContinuous, ae_eq_dirac, ProbabilityTheory.cond_mul_eq_inter', IsFiniteMeasureOnCompacts.smul, measure_inter_add_diff, eventually_nhds_zero_measure_vadd_diff_lt, nnnorm_indicatorConstLp_le, Conservative.ae_mem_imp_frequently_image_mem, count_withDensity', condExp_min_stopping_time_ae_eq_restrict_le_const, ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_compl_mutuallySingularSetSlice, Measure.map_right_mul_eq_modularCharacterFun_smul, ProbabilityTheory.Kernel.measurable_densityProcess_aux, Measure.measure_preimage_of_map_eq_self, Measure.dirac_apply_eq_zero_or_one, Measure.mapβ_apply_of_measurable, Measure.pi_closedBall, vadd_set_ae_eq, ae_restrict_biUnion_finset_eq, toMeasurable_def, Supermartingale.condExp_ae_le, Martingale.stoppedValue_ae_eq_condExp_of_le_const, integral_le_measure, addEquivAddHaarChar_smul_map, HasOuterApproxClosed.tendsto_lintegral_apprSeq, Lp.coeFn_lpSMul, withDensity_inv_same_le, VitaliFamily.covering, exists_lt_lowerSemicontinuous_integral_lt, IsAddFundamentalDomain.measure_eq_tsum, Lp.simpleFunc.coeFn_zero, L1.SimpleFunc.posPart_toSimpleFunc, measure_preimage_smul_of_nullMeasurableSet, ProbabilityTheory.iCondIndepSets_iff, Measure.compProd_zero_left, Measure.IicSnd_le_fst, lintegral_singleton', Measure.QuasiMeasurePreserving.tendsto_ae, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, condExpIndSMul_nonneg, measure_add_measure_eq, AEEqFun.compQuasiMeasurePreserving_toGerm, exp_neg_llr, Real.volume_eball, ProbabilityTheory.iIndep_iff, lintegral_unique, ae_restrict_eq, NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, Measure.dirac_apply_ne_one_iff_eq_zero, Measure.measurable_dirac, Measurable.smul_measure, Measure.inv_apply, MeasurePreserving.rnDeriv_comp_aeEq, ProbabilityTheory.IsRatCondKernelCDFAux.iInf_rat_gt_eq, Bornology.IsBounded.measure_lt_top, ProbabilityTheory.condExp_prod_ae_eq_integral_condDistribβ, ProbabilityTheory.Kernel.prodMkLeft_apply', exp_neg_llr', Real.volume_le_diam, le_toMeasure_apply, condExp_smul_of_aestronglyMeasurable_left, ProbabilityTheory.Kernel.lintegral_comap, aestronglyMeasurable_add_measure_iff, Add.sigmaFinite, MeasurableEmbedding.comap_apply, Measure.rnDeriv_singularPart, measure_add_closure_zero, ofReal_setIntegral_one, AEEqFun.coeFn_add, ContinuousLinearMap.coeFn_compLpL, isMulLeftInvariant_smul_nnreal, NumberField.mixedEmbedding.volume_negAt_plusPart, insert_ae_eq_self, NumberField.mixedEmbedding.convexBodyLT'_volume, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, ProbabilityTheory.moment_zero_measure, sum_measure_le_measure_univ, mem_ae_iff_prob_eq_oneβ, Measure.support_mem_ae, LipschitzOnWith.ae_differentiableWithinAt_of_mem_of_real, ProbabilityTheory.IsRatCondKernelCDFAux.le_one, ae_restrict_le_codiscreteWithin, ProbabilityTheory.uniformOn_add_compl_eq, ENNReal.count_const_le_le_of_tsum_le, Measure.dirac_apply_of_mem, IsProjectiveLimit.measure_cylinder, condLExp_bot_ae_eq, Conservative.measure_inter_frequently_image_mem_eq, diracProba_toMeasure_apply', tendsto_vadd_ae, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, essInf_eq_sSup, Isometry.hausdorffMeasure_preimage, toMeasure_applyβ, ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul, ProbabilityTheory.Kernel.withDensity_rnDeriv_le, LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_pi, SignedMeasure.rnDeriv_smul, instIsProbabilityMeasureHAddMeasureHSMulNNRealToNNRealSymm, le_trim, hausdorffMeasure_smul_right_image, SimpleFunc.measure_support_lt_top_of_lintegral_ne_top, ProbabilityTheory.Kernel.rnDeriv_lt_top, Measure.compProd_apply_prod, rnDeriv_tilted_left, ProbabilityTheory.Kernel.lintegral_piecewise, pdf_of_not_aemeasurable, Measure.count_apply_infinite, ProbabilityTheory.Kernel.continuous_integral_integral_comp, ProbabilityTheory.parallelProd_posterior_comp_copy_comp, Measure.compl_mem_cofinite, StieltjesFunction.measure_Icc, ProbabilityTheory.Kernel.fst_apply', MulAction.coe_aestabilizer, isProbabilityMeasure_iff, trim_measurableSet_eq, ZLattice.volume_image_eq_volume_div_covolume, measurable_measure_prodMk_left, Real.map_linearMap_volume_pi_eq_smul_volume_pi, IsFundamentalDomain.measure_eq_tsum', setLIntegral_const, ae_eq_of_integral_contMDiff_smul_eq, Measure.measure_toMeasurable_inter_of_sum, ProbabilityTheory.Kernel.const_zero, smul_mem_ae, Measure.AbsolutelyContinuous.ae_le, Measure.comap_apply_le, indicator_ae_eq_restrict_compl, Measure.restrict_union_add_interβ, measure_eq_zero_iff_eq_empty_of_smulInvariant, measure_inv_smul_symmDiff, Measure.MutuallySingular.add_right, ProbabilityTheory.Kernel.singularPart_eq_singularPart_measure, Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, ProbabilityTheory.Kernel.withDensity_apply, ProbabilityTheory.IsMarkovKernel.is_probability_measure', ProbabilityTheory.Kernel.iIndep.meas_iInter, ae_restrict_uIoc_iff, Measure.cofinite_le_ae, Measure.measure_isAddLeftInvariant_eq_vadd_of_ne_top, ProbabilityTheory.Kernel.ext_fun_iff, Measure.zero_le, mul_meas_ge_le_lintegralβ, Submartingale.zero_le_of_predictable', ProbabilityTheory.posterior_boolKernel_apply_false, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_indicator_mul_lintegral, ProbabilityTheory.Kernel.singularPart_of_subset_compl_mutuallySingularSetSlice, Measure.addHaar_smul_of_nonneg, condExpIndL1Fin_disjoint_union, Measure.measure_neg, Set.Subsingleton.measure_zero, aemeasurable_smul_measure_iff, Measure.rnDeriv_withDensity, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, LipschitzOnWith.ae_differentiableWithinAt_real, AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, MeasurePreserving.aeconst_preimage, ProbabilityTheory.setLIntegral_toKernel_prod, ProbabilityTheory.Kernel.lintegral_deterministic_prod, AEStronglyMeasurable.integral_condKernel, isAddRightInvariant_smul, Measure.MutuallySingular.add_left_iff, addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_aux, Finset.measure_zero, MeasurableEmbedding.map_apply, Measure.snd_univ, ProbabilityTheory.Fernique.measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self, ProbabilityTheory.Kernel.isProjectiveMeasureFamily_partialTraj, laverage_union, VitaliFamily.measure_le_mul_of_subset_limRatioMeas_lt, ae_measure_preimage_add_right_lt_top_of_ne_zero, Measure.mul_addHaarScalarFactor_smul, Measure.map_addHaar_smul, ProbabilityTheory.Kernel.setLIntegral_compProd, tendsto_measure_iInter_atTop, tendsto_measure_Ici_atBot, average_add_measure, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_comp, lintegral_indicator_const, Measure.ext_prodβ_iff, Measure.Subtype.volume_univ, Besicovitch.exists_disjoint_closedBall_covering_ae, eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ, ProbabilityTheory.Kernel.snd_apply', AECover.ae_tendsto_indicator, isTightMeasureSet_iff_exists_isCompact_measure_compl_le, measure_eq_iInf', Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, volume_pi_ball, Measure.finite_const_le_meas_of_disjoint_iUnionβ, ProbabilityTheory.Kernel.snd_apply, Measure.ae_count_iff, AEEqFun.compβ_toGerm, AEEqFun.sub_toGerm, measure_eq_measure_preimage_add_measure_tsum_Ico_zpow, tilted_zero_measure, Measure.count_apply_finset, AEFinStronglyMeasurable.ae_eq_zero_compl, inv_measure_univ_smul_eq_self, IsCompact.measure_lt_top, ProbabilityTheory.Kernel.sum_apply, measure_if, Measure.restrict_le_self, Measure.isMulLeftInvariant_eq_smul, hasFiniteIntegral_add_measure, ProbabilityTheory.measurable_condExpKernel, Integrable.integral_condDistrib, ProbabilityTheory.swap_compProd_posterior, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, Ioo_ae_eq_Ioc, EMetric.measure_ball_pos, Measure.map_apply_of_aemeasurable, ProbabilityTheory.avgRisk_const_left, measure_smul, ae_mem_iff_measure_eq, FiniteMeasure.mk_apply, Measure.iInf_rat_gt_prod_Iic, ProbabilityTheory.condDistrib_self, ProbabilityTheory.strong_law_aux7, ae_eq_zero_of_forall_setIntegral_eq_of_finStronglyMeasurable_trim, Measure.prod_add, tendsto_lintegral_thickenedIndicator_of_isClosed, integrable_prod_iff', Measure.addHaar_closedBall_mul_of_pos, ProbabilityTheory.iSup_bayesRisk_le_minimaxRisk, not_isFiniteMeasure_iff, PMF.toMeasure_apply_eq_one_iff, Measure.liftLinear_apply, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, ProbabilityTheory.uniformOn_inter_self, measure_inv_smul_union, ProbabilityTheory.covariance_zero_measure, ProbabilityTheory.Kernel.compProd_preimage_fst, Measure.singularPart_zero, MeasurePreserving.aeconst_comp, measure_zero_of_dimH_lt, Measure.mem_support_restrict, Measure.comp_assoc, ProbabilityTheory.condExp_ae_eq_integral_condDistrib', VAddInvariantMeasure.vadd_nnreal, IsUnifLocDoublingMeasure.ae_tendsto_average, ProbabilityTheory.Kernel.condExp_densityProcess, SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular, EuclideanSpace.volume_ball_fin_two, withDensity_pdf_le_map, MeasurePreserving.measure_preimage_le, Measure.instIsFiniteMeasureBindCoeKernelOfIsFiniteKernel, SimpleFunc.measure_preimage_lt_top_of_memLp, instIsZeroOrProbabilityMeasureOfNatMeasure, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, NumberField.mixedEmbedding.volume_eq_zero, ProbabilityTheory.Kernel.sectL_prodMkLeft, IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub, ProbabilityTheory.Kernel.traj_apply, Measure.count_univ, MemLp.condExpL2_ae_eq_condExp', Measure.IsHaarMeasure.smul, map_mul_right_ae, IsProjectiveMeasureFamily.congr_cylinder, ae_lt_top', Measure.InnerRegular.smul_nnreal, SimpleFunc.eLpNorm'_eq, measure_unionβ', Measure.le_iff, ProbabilityTheory.Kernel.iIndepSets_zero_right, indicatorConstLp_coeFn_notMem, NNRealRMK.le_rieszMeasure_of_tsupport_subset, Ergodic.iff_mem_extremePoints, HasFiniteIntegral.smul_measure, eLpNorm'_measure_zero_of_neg, measure_le_eq_lt, JordanDecomposition.smul_negPart, RealRMK.exists_open_approx, ProbabilityTheory.tilted_mul_apply_mgf, ProbabilityTheory.Kernel.prodMkRight_apply', EuclideanSpace.volume_ball, ProbabilityTheory.bayesRisk_le_iInf', Measure.real_def, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_mutuallySingular, integrable_add_measure, measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero, unitInterval.volume_Ioc, Conservative.ae_frequently_mem_of_mem_nhds, ProbabilityTheory.Kernel.iIndep_zero_right, Martingale.condExp_ae_eq, ContinuousMap.coeFn_toLp, AEEqFun.coeFn_star, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zero, AddCircle.addWellApproximable_ae_empty_or_univ, Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq, isAddRightInvariant_smul_nnreal, setLIntegral_pdf_le_map, ae_dirac_eq, Metric.measure_eball_pos, AECover.ae_eventually_mem, measure_preimage_smul_le, Measure.mconv_smul_right, SMulInvariantMeasure.smul_nnreal, AEEqFun.coeFn_zero, measure_lintegral_sub_measure, mulEquivHaarChar_smul_preimage, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_absolutelyContinuous, Measure.addHaar_preimage_linearMap, Metric.measure_closedBall_pos, isProbabilityMeasure_dite, Real.volume_Ici, IsProjectiveMeasureFamily.measure_univ_eq, AEEqFun.toGermAddMonoidHom_apply, Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, measure_preimage_vadd_le, withDensity_add_measure, Measure.sum_eq_zero, mul_meas_ge_le_lintegral, volume_pi_closedBall, Measurable.lintegral_kernel_prod_right, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real, Measure.measure_pos_of_nonempty_interior, measure_union_toMeasurable, ProbabilityTheory.condDistrib_comp_self, measure_biUnion_finsetβ, lpTrimToLpMeas_ae_eq, Antitone.measure_iInter, Real.volume_uIoo, eventually_nhds_one_measure_smul_diff_lt, Measure.sum_bool, rnDeriv_conv', ProbabilityTheory.measurableSet_kernel_integrable, AEEqFun.coeFn_compMeasurePreserving, ae_bdd_liminf_atTop_of_eLpNorm_bdd, measurable_measure_prodMk_right, addHaar_image_le_lintegral_abs_det_fderiv, exists_subordinate_pairwise_disjoint, exists_measurable_superset_iff_measure_eq_zero, ZLattice.volume_image_eq_volume_div_covolume', Measure.InnerRegularWRT.measure_eq_iSup, lintegral_finset_sum_measure, Measure.addHaar_preimage_continuousLinearEquiv, StronglyMeasurable.integral_kernel_prod_left'', measure_biUnion_finset, VitaliFamily.ae_tendsto_rnDeriv_of_absolutelyContinuous, Measure.countable_meas_pos_of_disjoint_iUnion, IsAddFundamentalDomain.covolume_eq_volume, ProbabilityTheory.bayesRisk_const_of_neZero, ProbabilityTheory.iCondIndepFun_iff, Measure.addHaar_ball_mul_of_pos, ProbabilityTheory.HasCondSubgaussianMGF.cgf_le, pdf.lintegral_eq_measure_univ, Measure.toOuterMeasure_le, IsAddFundamentalDomain.ae_covers, tendsto_measure_cthickening_of_isClosed, measure_eq_iInf, ProbabilityTheory.Kernel.id_apply, MemLp.meas_ge_lt_top', Real.volume_pi_Ico_toReal, Measure.prod_smul_right, ProbabilityTheory.uniformOn_univ, Measure.iSup_restrict_spanningSets, tendsto_measure_iInter_atBot, ae_mem_limsup_atTop_iff, tendstoInMeasure_iff_tendsto_toNNReal, ProbabilityTheory.integrable_kernel_prodMk_left, ProbabilityTheory.Kernel.compProd_apply_univ, charFun_zero_measure, ProbabilityTheory.avgRisk_const_left', JordanDecomposition.real_smul_posPart_neg, lintegral_fintype, Measure.id_comp, Measure.apply_eq_zero_of_isEmpty, setLIntegral_eq_zero_iff', TendstoInDistribution.tendsto, Measure.univ_pi_Iio_ae_eq_Iic, Measure.measure_Ioo_eq_zero, Measure.exists_positive_of_not_mutuallySingular, tsum_measure_preimage_singleton, Measure.isAddLeftInvariant_eq_smul_of_regular, setLIntegral_nnnorm_condExpIndSMul_le, AEEqFun.coeFn_inv, Real.volume_pi_le_diam_pow, Measure.setLIntegral_condKernel_univ_left, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Measure.restrict_applyβ, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, Conservative.ae_forall_image_mem_imp_frequently_image_mem, Measure.le_sum, Measure.addHaar_nnreal_smul, measure_diff, neg_ae, ProbabilityTheory.uniformOn_inter', ProbabilityTheory.Kernel.deterministic_apply', measure_Ioo_lt_top, innerRegularWRT_isCompact_isClosed_measure_ne_top_of_group, Measure.WeaklyRegular.smul, martingalePart_add_ae_eq, AEMeasurable.ae_eq_of_forall_setLIntegral_eq, measure_eq_sub_vadd, ProbabilityTheory.Kernel.boolKernel_true, ae_nonneg_of_forall_setIntegral_nonneg, Measure.addHaar_submodule, MeasurableSet.measure_eq_iSup_isClosed_of_ne_top, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, VitaliFamily.ae_tendsto_rnDeriv, DomMulAct.smul_Lp_ae_eq, measure_inter_neg_vadd, IsCompact.exists_open_superset_measure_lt_top, Measure.FiniteAtFilter.inf_ae_iff, Measure.addHaar_singleton_add_smul_div_singleton_add_smul, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, Measure.OuterRegular.smul, AEEqFun.div_toGerm, PMF.toMeasure_apply_eq_of_inter_support_eq, Measure.compProd_add_left, ProbabilityTheory.iIndepSet_iff, IsAddFundamentalDomain.measure_eq_tsum', measure_add_lintegral_eq, measure_diff', ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, ae_const_le_iff_forall_lt_measure_zero, AEDisjoint.exists_disjoint_diff, ProbabilityTheory.Kernel.borelMarkovFromReal_apply, measure_toMeasurable_union, MeasuredSets.continuous_measure, Measure.FiniteAtFilter.eventually, ProbabilityTheory.Kernel.lintegral_parallelComp_symm, Set.exists_isOpen_le_add, ProbabilityTheory.strong_law_aux4, ProbabilityTheory.Kernel.measure_le_bound, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, ProbabilityTheory.condVar_neg, tilted_of_not_integrable, Measure.le_map_apply_image, StieltjesFunction.measure_add, ProbabilityTheory.Kernel.lintegral_id, PreErgodic.prob_eq_zero_or_one, FiniteMeasure.prod_apply_symm, Integrable.coeFn_toL1, Measure.smul_apply, measure_inv_smul_inter, average_eq', SimpleFunc.lintegral_add, sum_measure_singleton, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd', ProbabilityTheory.uniformOn_union, Measure.ae_measure_lt_top, ProbabilityTheory.condVar_bot_ae_eq, VAddInvariantMeasure.zero, ProbabilityTheory.Kernel.const_add, Measure.inv_rnDeriv_aux, tendstoInMeasure_ae_unique, tilted_zero', IsTightMeasureSet_iff_exists_isCompact_measure_compl_le, LipschitzWith.ae_differentiableAt_of_real, Submartingale.ae_tendsto_limitProcess, measure_union_neg_vadd, ae_eq_of_setLIntegral_prod_eq, MeasurableEmbedding.comap_preimage, Measure.le_count_apply, ProbabilityTheory.Kernel.setLIntegral_compProd_univ_right, eq_zero_or_isProbabilityMeasure, Measure.IsCondKernel.isProbabilityMeasure, FiniteMeasure.coeFn_mk, Measure.AbsolutelyContinuous.add, Measure.instNeZeroENNRealCoeSetUniv, ProbabilityMeasure.mk_apply, ProbabilityTheory.indepFun_iff_measure_inter_preimage_eq_mul, ProbabilityMeasure.map_apply', Measure.prod_comp_left, condExp_restrict_ae_eq_restrict, ProbabilityTheory.iIndepFun.meas_iInter, hausdorffMeasure_of_dimH_lt, aemeasurable_zero_measure, smul_set_ae_eq, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atBot, addEquivAddHaarChar_smul_eq_comap, UnifTight.exists_measurableSet_indicator, Measure.lintegral_join_le, hasFiniteIntegral_prod_iff, Conservative.inter_frequently_image_mem_ae_eq, exists_null_frontiers_thickening, ProbabilityTheory.Kernel.traj_map_frestrictLe_apply, ProbabilityTheory.iIndepFun.condExp_natural_ae_eq_of_lt, measureUnivNNReal_zero, Measure.MutuallySingular.measure_compl_nullSet, Measure.restrict_iUnion_apply_ae, pdf.eq_of_map_eq_withDensity', Measure.tendsto_IicSnd_atTop, Lp.coeFn_negPart, isZeroOrProbabilityMeasure_iff, Integrable.prod_left_ae, integrableOn_singleton_iff, Measure.ae_smul_measure_le, SimpleFunc.lintegral_eq_of_subset, ProbabilityTheory.condVar_of_aestronglyMeasurable, mulEquivHaarChar_smul_eq_comap, Measure.add_left_inj, ProbabilityTheory.IsSetBernoulli.ae_subset, Measure.measure_Ioo_pos, measure_ball_lt_top, Measure.support_eq_sInter, measure_sUnionβ, ProbabilityTheory.IsRatCondKernelCDFAux.isRatStieltjesPoint_ae, measure_symmDiff_eq, StieltjesFunction.measure_Ioc, Measure.rnDeriv_withDensityβ, ProbabilityTheory.uncenteredCovarianceBilin_zero, eLpNorm_indicator_const', AEEqFun.coeFn_posPart, ProbabilityTheory.Kernel.finset_sum_apply, IsUpperSet.null_frontier, ae_restrict_iff, llr_tilted_left, Measure.infinitePi_cylinder, projectiveFamilyFun_congr, AEFinStronglyMeasurable.ae_eq_mk, ae_withDensity_iff', Measure.comp_smul, lintegral_le_meas, ProbabilityTheory.setLIntegral_condKernel_eq_measure_prod, Measure.zero_mconv, Measurable.map_prodMk_right, Measure.sum_zero, eLpNorm'_eq_zero_iff, Measure.isAddLeftInvariant_eq_smul_of_innerRegular, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, Submartingale.exists_ae_tendsto_of_bdd, JordanDecomposition.real_smul_negPart_neg, measure_le_integral_pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, Measure.MutuallySingular.disjoint_ae, ProbabilityTheory.posterior_id, FiniteMeasure.map_apply', measure_union, lintegral_insert, Measure.hausdorffMeasure_apply, Conservative.measure_mem_forall_ge_image_notMem_eq_zero, Ergodic.mem_extremePoints_measure_univ_eq, left_measure_le_of_levyProkhorovEDist_lt, Measure.eq_zero_of_isEmpty, Measure.map_const, ProbabilityTheory.Kernel.measure_eq_zero_or_one_or_top_of_indepSet_self, PMF.toMeasure_injective, AlternatingMap.measure_def, Submartingale.upcrossings_ae_lt_top', maximal_ineq, AEEqFun.mk_toGerm, Measure.support_zero, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', ProbabilityTheory.Kernel.IsProper.setLIntegral_inter_eq_indicator_mul_setLIntegral, withDensity_add_right, eLpNormEssSup_lt_top_iff_isBoundedUnder, distribHaarChar_eq_div, blimsup_cthickening_ae_eq_blimsup_thickening, MemLp.coeFn_toLp, dirac_withDensity', IsProbabilityMeasure.ae_neBot, exists_seq_tendstoInMeasure_atTop_iff, ProbabilityTheory.Kernel.iIndep.ae_isProbabilityMeasure, Measure.count_apply_finite', tendsto_measure_Icc_nhdsWithin_right', Measure.sub_apply_eq_zero_of_isHahnDecomposition, measure_Ico_lt_top, Measure.dirac_apply, exists_measurable_superset_forall_eq, Measure.absolutelyContinuous_zero_iff, hausdorffMeasure_orthogonalProjection_le, ProbabilityTheory.cond_eq_zero, QuasiErgodic.zero_measure, lintegral_indicator_one, ProbabilityTheory.Kernel.lintegral_prod_deterministic, Measure.mapβ_eq_zero_iff, ProbabilityTheory.Kernel.measure_sum_seq, ProbabilityTheory.meas_ge_le_evariance_div_sq, exists_setLIntegral_compl_lt, IsAddFundamentalDomain.measure_addFundamentalFrontier, Real.map_volume_mul_right, diracProba_toMeasure_apply, Measure.haarScalarFactor_smul_smul, ae_restrict_iff', NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ, Measure.completion_apply, Measure.le_join_apply, measure_preimage_smul, ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSlice, Measure.rnDeriv_smul_left, Measure.instIsScalarTower, measure_pos_iff_nonempty_of_isMulLeftInvariant, SimpleFunc.measure_lt_top_of_memLp_indicator, hausdorffMeasure_smul, Measure.restrict_apply_eq_zero', Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, pow_mul_meas_ge_le_eLpNorm, ProbabilityTheory.Kernel.measurable, Measure.exists_measure_inter_spanningSets_pos, VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, Measure.setLIntegral_compProd, Set.measure_eq_iInf_isOpen, eLpNorm_const, Measure.mkMetric_le_liminf_sum, ProbabilityTheory.Kernel.measurable_coe, ProbabilityTheory.Kernel.withDensity_rnDeriv_mutuallySingularSetSlice, Measure.MeasureDense.nonempty', ProbabilityTheory.Kernel.comapRight_apply', null_iff_of_isAddLeftInvariant, curveIntegralFun_trans_aeeq_left, piecewise_ae_eq_restrict, Measure.toOuterMeasure_top, ProbabilityTheory.Kernel.eLpNorm_density_le, polarCoord_source_ae_eq_univ, ProbabilityTheory.cond_apply', distribHaarChar_mul, Measure.addHaar_preimage_linearEquiv, ProbabilityTheory.Kernel.lintegral_comp, Measure.hausdorffMeasure_le_one_of_subsingleton, ProbabilityTheory.absolutelyContinuous_boolKernel_comp_right, measure_eq_inducedOuterMeasure, IsAddFoelner.tendsto_nhds_mean, pdf.IsUniform.integral_eq, LipschitzOnWith.hausdorffMeasure_image_le, MeasurableEquiv.map_measurableEquiv_injective, ProbabilityTheory.Kernel.condKernel_def, hausdorffMeasure_affineSegment, IsCompact.measure_eq_biInf_integral_hasCompactSupport, Measure.rnDeriv_restrict_self, Measure.MutuallySingular.self_iff, Lp.coeFn_zero, ProbabilityMeasure.toMeasure_injective, ProbabilityTheory.Kernel.setIntegral_piecewise, Complex.volume_ball, toMeasure_apply, ProbabilityTheory.ae_cond_of_forall_mem, ProbabilityTheory.iIndepSet_iff_meas_biInter, StieltjesFunction.measure_Iio, measureReal_def, StieltjesFunction.measure_smul, Measure.restrict_sub_eq_restrict_sub_restrict, StieltjesFunction.ae_hasDerivAt, le_ae_restrict, OuterMeasure.toMeasure_zero, ProbabilityTheory.strong_law_aux1, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, SimpleFunc.lintegral_finset_sum, ProbabilityTheory.measure_condCDF_Iic, AEEqFun.mk_eq_mk, ProbabilityTheory.indepSet_iff_measure_inter_eq_mul, MeasurableEmbedding.ae_map_iff, measure_symmDiff_neg_vadd, eLpNorm_le_eLpNorm_mul_rpow_measure_univ, IsFundamentalDomain.measure_fundamentalInterior, IsCompact.measure_lt_top_of_nhdsWithin, PMF.toMeasure_bindOnSupport_apply, ProbabilityTheory.Kernel.densityProcess_fst_univ, tendsto_measure_iUnion_accumulate, Integrable.measure_le_lt_top, condExpIndL1Fin_ae_eq_condExpIndSMul, Measure.rnDeriv_withDensity_left_of_absolutelyContinuous, ProbabilityTheory.cond_empty, lintegral_abs_det_fderiv_eq_addHaar_imageβ, lintegral_pos_iff_support, sfiniteSeq_zero, Lp.norm_measure_zero, Measure.sum_of_isEmpty, ProbabilityTheory.measurable_measure_condCDF, aestronglyMeasurable_iff_nullMeasurable_separable, AddContent.measureCaratheodory_eq_inducedOuterMeasure, LipschitzWith.coeFn_compLp, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Measure.ae_mono', ProbabilityTheory.strong_law_ae_simpleFunc_comp, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, ProbabilityTheory.Kernel.comap_apply, IsProjectiveLimit.measure_univ_unique, SignedMeasure.rnDeriv_neg, Integrable.smul_measure, ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkRight, ProbabilityTheory.IndepFun_iff, Measure.addHaar_closedBall, OuterMeasure.coe_mkMetric, Measure.compProd_of_not_sfinite, ProbabilityTheory.Kernel.sectL_apply, submartingale_iff_condExp_sub_nonneg, Lp.coeFn_neg, tendsto_measure_cthickening_of_isCompact, condExp_bilin_of_stronglyMeasurable_right, Measure.Regular.smul_nnreal, IsFiniteMeasureOnCompacts.lt_top_of_isCompact, measure_preimage_eq_zero_iff_of_countable, Martingale.condExp_stopping_time_ae_eq_restrict_eq_const, Lp.coeFn_abs, VitaliFamily.ae_eventually_measure_pos, ProbabilityTheory.posterior_posterior, eLpNorm_indicator_constβ, AEEqFun.mul_toGerm, Measure.sub_def, PMF.toMeasure_apply_inter_support, Measure.infinitePi_singleton, isZeroOrProbabilityMeasureSMul, ProbabilityTheory.lintegral_preCDF_fst, Measure.coe_completion, VitaliFamily.measure_limRatioMeas_top, Monotone.measure_iUnion, ProbabilityTheory.Kernel.zero_apply, Measure.addHaarScalarFactor_domSMul, measure_preimage_add_right, setLIntegral_smul_measure, AEStronglyMeasurable.isSeparable_ae_range, Measure.singularPart_add_rnDeriv, ProbabilityTheory.condDistrib_const, isLocallyFiniteMeasureSMulNNReal, ProbabilityTheory.Kernel.lintegral_prodMkLeft, FiniteMeasure.toMeasure_smul, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop, Measure.measurable_lintegral, Measure.dirac_compProd_apply, Measure.AbsolutelyContinuous.smul, AEEqFun.zpow_toGerm, AEStronglyMeasurable.integral_condDistrib, integral_zero_measure, AEEqFun.comp_toGerm, ae_eq_of_forall_setLIntegral_eq_of_sigmaFiniteβ, Measure.prod_comp_right, Measure.measure_prod_null, ProbabilityTheory.evariance_eq_zero_iff, AlternatingMap.measure_parallelepiped, blimsup_thickening_mul_ae_eq, Measure.MutuallySingular.restrict_compl_nullSet, ProbabilityTheory.Kernel.iIndepFun.meas_iInter, Measure.count_apply_eq_top', Measure.ext_iff_singleton, Real.volume_univ, Measure.measure_support_eq_zero_iff, Measure.finite_const_le_meas_of_disjoint_iUnion, eventually_add_left_iff, essSup_smul_measure, countable_meas_le_ne_meas_lt, ProbabilityTheory.Kernel.setIntegral_density, tendsto_measure_compl_closedBall_of_isTightMeasureSet, exp_llr_of_ac, IsAddFoelner.tendsto_meas_vadd_symmDiff, isFiniteMeasureSMulNNReal, Measure.compProd_zero_right, Measure.measure_pos_of_mem_nhds, Integrable.smul_measure_nnreal, ae_eq_condLExpβ, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, ProbabilityMeasure.val_eq_to_measure, Lp.coeFn_sub, ProbabilityTheory.strong_law_aux2, eventually_mul_right_iff, AEEqFun.coeFn_zpow, measure_add_measure_complβ, condLExp_smul', ProbabilityTheory.uniformOn_compl, tendstoInMeasure_iff_enorm, ProbabilityTheory.condDistrib_fst_prod, Measure.compProd_of_not_isSFiniteKernel, integrable_zero_measure, Lp.meas_ge_le_mul_pow_enorm, IsClosed.measure_eq_univ_iff_eq, Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, measure_average_le_pos, ProbabilityTheory.Kernel.integral_integral_indicator, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, withDensity_smul_measure, Measure.join_apply, restrict_compl_sigmaFiniteSetWRT, ProbabilityTheory.posterior_comp_self, ProbabilityTheory.Kernel.indepFun_zero_right, Measure.tsum_indicator_apply_singleton, LipschitzWith.hausdorffMeasure_image_le, right_measure_le_of_levyProkhorovEDist_lt, volume_regionBetween_eq_integral, mem_map_indicator_ae_iff_mem_map_restrict_ae_of_zero_mem, ContinuousLinearMap.coeFn_compLp, ProbabilityTheory.setLIntegral_condCDF, Measure.restrictβ_apply, measure_setAverage_le_pos, withDensity_apply', MeasurableSet.exists_isCompact_isClosed_lt_add, ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self, ProbabilityTheory.Kernel.pow_succ_apply_eq_lintegral, ProbabilityTheory.Kernel.iIndepFun.meas_biInter, ProbabilityTheory.Kernel.IndepFun.measure_inter_preimage_eq_mul, measure_lt_top_of_isCompact_of_isAddLeftInvariant', AEDisjoint.diff_ae_eq_left, Measure.map_smul, ProbabilityTheory.posterior_eq_withDensity_of_countable, ProbabilityTheory.Kernel.lintegral_deterministic, ProbabilityTheory.IsFiniteKernel.exists_univ_le, lintegral_nnnorm_condExpIndSMul_le, ProbabilityTheory.avgRisk_const_right', Measure.InnerRegularCompactLTTop.smul_nnreal, measure_le_average_pos, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, volume_preimage_coe, Measure.ennreal_smul_eq_zero, measureReal_zero_apply, ProbabilityTheory.iIndep.meas_iInter, ae_not_liouville, ProbabilityTheory.measure_condCDF_univ, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, withDensity_eq_iff_of_sigmaFinite, AEDisjoint.measure_diff_right, Measure.lintegral_join, measure_eq_trim, AEEqFun.zero_toGerm, InnerProductSpace.volume_closedBall, Measure.zero_sub, Measure.compProd_eq_zero_iff, measure_preimage_vadd, Measure.IicSnd_mono, ProbabilityTheory.Kernel.measurable_singularPart, Directed.measure_iInter, ProbabilityTheory.Kernel.comapRight_apply, eLpNorm_const_lt_top_iff, Measure.IicSnd_univ, measure_Ioc_lt_top, Measure.le_dirac_apply, ProbabilityTheory.Kernel.setLIntegral_piecewise, Measure.volumeIoiPow_apply_Iio, ProbabilityTheory.integrable_toReal_condDistrib, Measure.copy_comp_map, Measure.countable_meas_level_set_posβ, ProbabilityTheory.Kernel.comp_apply', Martingale.ae_eq_condExp_limitProcess, Measure.IsEverywherePos.smul_measure_nnreal, ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero, Real.hausdorffMeasure_of_finrank_lt, eLpNorm'_measure_zero_of_exponent_zero, ProbabilityTheory.bayesRisk_zero_right, prob_compl_eq_one_sub, ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv, ProbabilityTheory.Kernel.integral_piecewise, null_iff_of_isMulLeftInvariant, ProbabilityTheory.strong_law_ae_real, ae_restrict_iff'β, withDensity_smul, ProbabilityTheory.IdentDistrib.measure_mem_eq, lintegral_abs_det_fderiv_le_addHaar_image_aux2, Measure.haveLebesgueDecompositionSMulRight, IsFundamentalDomain.measure_fundamentalFrontier, tendsto_measure_smul_diff_isCompact_isClosed, InnerProductSpace.volume_closedBall_of_dim_odd, ProbabilityTheory.strong_law_aux5, IsAddFundamentalDomain.addProjection_respects_measure_apply, Measure.measure_sub_rnDeriv, NumberField.mixedEmbedding.fundamentalCone.compactSet_ae, StieltjesFunction.measure_Ico, FiniteMeasure.ennreal_mass, ProbabilityTheory.Kernel.parallelComp_apply, ProbabilityTheory.Kernel.compProd_apply_eq_compProd_sectR, ProbabilityTheory.uniformOn_singleton, lmarginal_image, Lp.coeFn_posPart, Measure.MutuallySingular.rnDeriv_ae_eq_zero, ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkLeft, pi_polarCoord_symm_target_ae_eq_univ, Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, Measure.add_prod, ProbabilityTheory.IsRatCondKernelCDF.isRatStieltjesPoint_ae, Measure.count_apply_lt_top', isTightMeasureSet_iff_tendsto_measure_norm_gt, Measure.tendsto_eval_ae_ae, AEEqFun.coeFn_pow, BoxIntegral.unitPartition.volume_box, Measure.measure_univ_eq_zero, measure_mul_lintegral_eq, Measure.addHaar_closedBall_mul, Complex.volume_sum_rpow_lt_one, Measure.tendsto_IicSnd_atBot, Measure.IsAddHaarMeasure.nnreal_smul, IsFundamentalDomain.measure_eq, eLpNormEssSup_eq_zero_iff, Measure.restrict_union_add_inter', ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero', Measure.measure_Ioi_pos, ProbabilityTheory.Kernel.iIndepSets_singleton_iff, measure_iUnion_eq_iSup_accumulate, ProbabilityTheory.setBernoulli_ae_subset, Measure.compProd_smul_left, Measure.mul_haarScalarFactor_smul, ae_eq_of_forall_setIntegral_eq_of_sigmaFinite', AddAction.aeconst_of_aestabilizer_eq_top, measure_neg_vadd_union, Measure.pi_empty_univ, IsOpen.ae_eq_zero_of_integral_contMDiff_smul_eq_zero, Measure.snd_add, Measure.setLIntegral_condKernel_univ_right, ProbabilityTheory.condDistrib_map, ProbabilityTheory.setLIntegral_condDistrib_of_measurableSet, Measure.addHaarScalarFactor_smul_congr', blimsup_cthickening_mul_ae_eq, Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_measurableSet, Measure.ext_iff', ProbabilityTheory.Kernel.compProd_eq_iff, NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, Lp.ae_eq_of_forall_setIntegral_eq, llr_smul_right, ProbabilityTheory.Kernel.compProd_apply, Measure.ae.neBot, IsOpen.ae_eq_zero_of_integral_smooth_smul_eq_zero, condExp_indep_eq, MeasurableEquiv.gaussianReal_map_symm_apply, ProbabilityTheory.IndepSets_iff, FinStronglyMeasurable.fin_support_approx, ProbabilityTheory.cond_mul_eq_inter, ae_map_mem_range, ProbabilityTheory.IsCondKernelCDF.lintegral, Measure.sigmaFinite_iff_measure_singleton_lt_top, ProbabilityTheory.Kernel.measurable', Measure.sub_le, ae_le_of_forall_setIntegral_le, ProbabilityTheory.Kernel.withDensity_apply', ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, Measure.rnDeriv_withDensity_rnDeriv, toFinite_apply_eq_zero_iff, lpMeasToLpTrim_ae_eq, measure_sUnion, AEStronglyMeasurable.prodMk_left, Martingale.eq_condExp_of_tendsto_eLpNorm, Measure.count_apply_finite, ProbabilityTheory.Kernel.const_apply, Measure.compProd_add_right, Measure.addHaar_ball, AEMeasurable.ae_mem_imp_eq_mk, AEMeasurable.smul_measure, eLpNorm_sub_le_of_dist_bdd, integrable_average, laverage_add_measure, IsAddFundamentalDomain.measure_eq_tsum_of_ac, measure_eq_extend, StieltjesFunction.measure_Iic, lpNorm_smul_measure_of_ne_top, Measure.map_applyβ, ae_le_of_forall_setLIntegral_le_of_sigmaFinite, Measure.sub_self, NullMeasurableSet.toMeasurable_ae_eq, Measure.exists_ae_subset_biUnion_countable, ProbabilityTheory.Kernel.rnDeriv_add, Measure.instSFiniteBindCoeKernelOfIsSFiniteKernel, eLpNorm_one_add_measure, AEMeasurable.ae_eq_mk, ProbabilityTheory.setLIntegral_preimage_condDistrib, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, Measure.tprod_tprod, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, AddCircle.closedBall_ae_eq_ball, measure_union', Measure.bind_zero_right', IntervalIntegrable.ae_hasDerivAt_integral, ProbabilityTheory.eq_condKernel_of_kernel_eq_compProd, Measure.prod_zero, Measure.mconv_smul_left, ae_eq_zero_of_eLpNorm'_eq_zero, AddAction.mem_aestabilizer, rnDeriv_tilted_right, exists_measurable_superset, eventuallyConst_neg_set_ae, Measure.toSphere_eq_zero_iff_finrank, ProbabilityTheory.Kernel.sum_apply', Measure.add_sub_of_mutuallySingular, Measure.ae_compProd_iff, Measure.instSMulCommClass, ProbabilityTheory.Kernel.IndepSet.measure_inter_eq_mul, JordanDecomposition.real_smul_negPart_nonneg, Real.volume_uIoc, smul_set_ae_le, measure_setLAverage_le_pos, Measure.HaveLebesgueDecomposition.add_left, ae_eq_restrict_iff_indicator_ae_eq, ProbabilityTheory.strong_law_ae_of_measurable, measure_isOpen_pos_of_smulInvariant_of_ne_zero, Measure.absolutelyContinuous_compProd_right_iff, measure_eq_zero_iff_eq_empty_of_vaddInvariant, Measure.map_zero, eLpNorm_smul_measure_of_ne_zero, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, Measure.snd_apply, Measure.dirac_unit_compProd, unitInterval.volume_uIoc, ProbabilityMeasure.measurableSet_isProbabilityMeasure, Measure.fst_zero, condExp_sub, FiniteMeasure.toMeasure_zero, Measure.MutuallySingular.disjoint, Measure.join_zero, ProbabilityTheory.Kernel.iIndepFun.ae_isProbabilityMeasure, ProbabilityTheory.Kernel.lintegral_deterministic', condExpIndSMul_ae_eq_smul, PreErgodic.ae_mem_or_ae_notMem, isMulRightInvariant_smul_nnreal, Measure.ae_pi_le_pi, Measure.addHaar_closedBall_center, Lp.dense_hasCompactSupport_contDiff, Real.volume_Ioi, Measure.instIsCentralScalar, ProbabilityTheory.Kernel.swapLeft_apply', Measure.toENNRealVectorMeasure_apply_measurable, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, IsFundamentalDomain.ae_covers, FiniteMeasure.measurableSet_isFiniteMeasure, ProbabilityTheory.condIndepFun_iff, Measure.rnDeriv_self, lpMeas.ae_fin_strongly_measurable', Real.volume_Ioo, ProbabilityMeasure.null_iff_toMeasure_null, prob_add_prob_compl, isTightMeasureSet_singleton_of_innerRegular, tilted_of_not_aemeasurable, Metric.measure_ball_pos, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, ProbabilityTheory.absolutelyContinuous_boolKernel_comp_left, ProbabilityTheory.mgf_smul_measure, isAddLeftInvariant_smul_nnreal, ProbabilityMeasure.prod_apply_symm, ProbabilityTheory.lintegral_condKernel_mem, Measure.map_right_add_eq_addModularCharacterFun_vadd, ProbabilityTheory.IndepSet.measure_inter_eq_mul, measure_preimage_mul_right, ProbabilityTheory.compProd_posterior_eq_swap_comp, ProbabilityTheory.Kernel.setLIntegral_const, ae_eq_condExp_of_forall_setIntegral_eq, StronglyMeasurable.integral_kernel_prod_left', VitaliFamily.ae_tendsto_limRatioMeas, weightedSMul_smul_measure, ProbabilityTheory.Kernel.rnDeriv_self, IsAntichain.volume_eq_zero, ProbabilityTheory.Kernel.measurable_kernel_prodMk_right, AEEqFun.compMeasurePreserving_toGerm, HasFiniteIntegral.add_measure, Submartingale.exists_ae_trim_tendsto_of_bdd, MeasurableSet.exists_isOpen_symmDiff_lt, Martingale.stoppedValue_ae_eq_condExp_of_le_const_of_countable_range, hausdorffMeasure_homothety_preimage, Measure.restrict_apply', ProbabilityTheory.Kernel.lmarginalPartialTraj_succ, eventually_add_right_iff, VAddInvariantMeasure.measure_preimage_vadd, IsOpen.ae_eq_zero_of_integral_smooth_smul_eq_zero', Measure.pi_Iio_ae_eq_pi_Iic, ProbabilityTheory.gaussianReal_apply_eq_integral, MeasurePreserving.measure_symmDiff_preimage_iterate_le, ENNReal.ae_eq_zero_of_lintegral_rpow_eq_zero, Measure.prodMkLeft_comp_compProd, measure_union_add_interβ, ProbabilityTheory.IsRatCondKernelCDF.mono, VitaliFamily.eventually_measure_lt_top, ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, ProbabilityTheory.Kernel.measure_mutuallySingularSetSlice, Measure.bind_zero_left, StronglyMeasurable.ae_eq_trim_iff, VitaliFamily.ae_tendsto_average, RealRMK.le_rieszMeasure_tsupport_subset, lpTrimToLpMeasSubgroup_ae_eq, NumberField.mixedEmbedding.convexBodySum_volume, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, Measure.isFiniteMeasure_sub, Measurable.setLIntegral_kernel_prod_right, ae_restrict_iUnion_iff, FiniteMeasure.measurable_fun_prod, VAddInvariantMeasure.vadd, SimpleFunc.finMeasSupp_iff, indicator_ae_eq_restrict, le_measure_diff, ProbabilityTheory.Kernel.comp_apply_univ_le, Lp.coeFn_inf, lintegral_deriv_eq_volume_image_of_monotoneOn, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, IsLowerSet.null_frontier, volume_image_subtype_coe, ProbabilityTheory.uniformOn_disjoint_union, ProbabilityTheory.IsRatCondKernelCDF.integrable, Measure.ofMeasurable_apply, eLpNorm_smul_measure_of_ne_zero', tilted_apply_eq_ofReal_integral', measure_le_measure_union_right, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_univ_le_one, NullMeasurableSet.exists_measurable_superset_ae_eq, measure_add_right_null, tendsto_measure_Ico_atTop, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le_exp_add, Measure.singularPart_of_not_haveLebesgueDecomposition, exists_upperSemicontinuous_lt_integral_gt, Measure.top_add, ProbabilityTheory.Kernel.apply_congr_of_mem_measurableAtom, Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_topβ, eventuallyConst_vadd_set_ae, isTightMeasureSet_iff_tendsto_measure_compl_closedBall, Measure.FiniteAtFilter.exists_mem_basis, withDensity_const, aemeasurable_add_measure_iff, eLpNormEssSup_measure_zero, ProbabilityTheory.condKernel_const, Measure.rnDeriv_add', Measurable.map_prodMk_left, ProbabilityTheory.Kernel.lintegral_compProd, MeasurableSet.exists_isClosed_diff_lt, Measure.measure_preimage_inv, Measure.pi_pi, Measure.toSignedMeasure_zero, Measure.setLIntegral_rnDeriv_le, AEEqFun.coeFn_div, innerRegularWRT_isCompact_isClosed_measure_ne_top_of_addGroup, Integrable.condDistrib_ae_map, integrable_mconv_iff, Measure.restrict_applyβ', ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib', Measure.join_map_join, ProbabilityMeasure.coeFn_mk, Measure.singularPart_smul_right, rnDeriv_tilted_left_self, measure_eq_top_of_lintegral_ne_top, eventually_div_right_iff, lpNorm_eq_zero, measure_preimage_snd_singleton_eq_tsum, measure_union_inv_smul, MeasuredSets.edist_def, measure_unitBall_eq_integral_div_gamma, Lp.simpleFunc.toSimpleFunc_eq_toFun, ProbabilityTheory.Kernel.parallelComp_apply_univ, HolderOnWith.hausdorffMeasure_image_le, mul_meas_ge_le_pow_eLpNorm, ProbabilityTheory.Kernel.lintegral_parallelComp, dimH_def, ProbabilityTheory.cgf_zero_measure, Measure.sum_restrict_le, Measure.instSubsingleton, Integrable.condExpKernel_ae, Measure.ae_ae_comm, setLIntegral_le_meas, Measure.measure_inv, Real.volume_pi_closedBall, lintegral_indicator_constβ, eLpNorm'_const, Measure.exists_isOpen_measure_lt_top, IsCompact.exists_isOpen_lt_add, tendsto_measure_thickening_of_isClosed, Measure.restrict_eq_self, uIoc_ae_eq_interval, Integrable.integral_norm_condKernel, Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, tendsto_measure_biUnion_Ici_zero_of_pairwise_disjoint, ae_not_liouvilleWith, ProbabilityTheory.Kernel.densityProcess_def, MeasurableEquiv.map_ae, Measure.mconv_zero, LipschitzOnWith.ae_differentiableWithinAt_of_mem_pi, OuterMeasure.toMeasure_eq_zero, Ico_ae_eq_Icc, Measurable.lintegral_kernel_prod_right', Measure.rnDeriv_pos', Measure.mconv_add, Measure.instIsZeroOrProbabilityMeasureBindCoeKernelOfIsZeroOrMarkovKernel, measure_iUnion_toMeasurable, eLpNormEssSup_ennreal_smul_measure, ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, integrable_finset_sum_measure, ProbabilityMeasure.prod_apply, PreErgodic.aeconst_set, Ergodic.mem_extremePoints, Lp.pow_mul_meas_ge_le_enorm, NullMeasurableSet.exists_measurable_subset_ae_eq, Measure.compProd_eq_parallelComp_comp_copy_comp, LipschitzOnWith.ae_differentiableWithinAt, condLExp_add_le, lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, StronglyMeasurable.integral_kernel, Measure.isAddLeftInvariant_eq_smul, Measure.rnDeriv_eq_zero, ae_restrict_uIoc_eq, ProbabilityTheory.Kernel.lmarginalPartialTraj_eq_lintegral_map, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div_of_integrable, ProbabilityTheory.Kernel.lintegral_swapLeft, StronglyMeasurable.integral_kernel_prod_left, Measure.restrict_union_le, ProbabilityTheory.setBernoulli_apply, forall_measure_preimage_add_right_iff, PMF.toMeasure_apply_eq_toOuterMeasure, ProbabilityTheory.HasCondSubgaussianMGF.mgf_le, ProbabilityTheory.Kernel.integral_withDensity, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div, EMetric.measure_closedBall_pos, FiniteMeasure.toMeasure_sum, ProbabilityTheory.evariance_zero_measure, LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_real, exp_llr, measure_union_add_inter', ProbabilityTheory.Kernel.const_comp, ProbabilityTheory.bayesRisk_const', ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot, ae_toFiniteAux, Measure.map_of_not_aemeasurable, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, indicatorConstLp_coeFn, ProbabilityTheory.Kernel.compProd_apply_prod, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div'_of_integrable, Measure.measure_Iio_pos, integrable_inv_smul_measure, eLpNorm_measure_zero, ProbabilityTheory.Kernel.partialTraj_compProd_eq_map_traj, weightedSMul_zero_measure, ProbabilityTheory.Kernel.iIndepSets.meas_iInter, ProbabilityTheory.Kernel.rnDeriv_withDensity, Measure.lt_iff, IsFoelner.tendsto_nhds_mean, Lp.simpleFunc.coeFn_nonneg, FiniteMeasure.toMeasureAddMonoidHom_apply, ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zero, exists_measure_iInter_lt, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd, integral_smul_measure, Measure.condKernel_apply, memLp_trim_of_mem_lpMeasSubgroup, Measure.restrict_compl_add_restrict, AEStronglyMeasurable.ae_mem_imp_eq_mk, Module.Basis.addHaar_self, ProbabilityTheory.Kernel.measurable_kernel_prodMk_left, StieltjesFunction.measure_Iio_of_tendsto_atBot_atBot, IntegrableAtFilter.inf_ae_iff, IsClosed.ae_eq_univ_iff_eq, Measure.le_restrict_apply, volume_regionBetween_eq_lintegral, AEDisjoint.measure_diff_left, measure_mul_setLAverage, prob_compl_eq_zero_iffβ, IsOpen.ae_eq_zero_of_integral_contMDiff_smul_eq_zero', Real.volume_preimage_mul_right, ProbabilityTheory.Kernel.setLIntegral_rnDerivAux, ProbabilityTheory.Kernel.comp_boolKernel, ae_eq_restrict_iUnion_iff, isAddFoelner_iff, Measure.neg_apply, Measure.toENNRealVectorMeasure_zero, measure_closedBall_lt_top, Measure.lintegral_compProd, Measure.singularPart_eq_zero_of_ac, InnerProductSpace.volume_ball_of_dim_even, PMF.toMeasure_mono, Measure.ae_sum_iff', Measure.addHaar_singleton, EuclideanSpace.volume_closedBall, Measure.instHaveLebesgueDecompositionZeroLeft, Measure.conv_smul_right, PreErgodic.zero_measure, ENNReal.essSup_eq_zero_iff, condExp_min_stopping_time_ae_eq_restrict_le, Filter.HasBasis.mem_measureSupport, Measure.addHaarScalarFactor_smul, Measure.haveLebesgueDecomposition_spec, ProbabilityMeasure.limsup_measure_closed_le_of_tendsto, ENNReal.ae_le_essSup, condExpL2_comp_continuousLinearMap, Measure.add_conv, Lp.coeFn_star, Measure.toSignedMeasure_restrict_sub, Measure.add_toOuterMeasure, withDensity_smul', toFinite_zero, ProbabilityTheory.Kernel.comap_apply', Measure.withDensity_sub, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, exists_isCompact_closure_measure_compl_lt, map_div_right_ae, Integrable.integral_condKernel, Submartingale.ae_le_condExp, ae_restrict_union_eq, MemLp.meas_ge_lt_top_enorm, Measure.count_injective_image, Measure.infinitePi_pi_univ, toReal_rnDeriv_tilted_right, ProbabilityTheory.aestronglyMeasurable_integral_condExpKernel, Measure.support_add, Measure.setLIntegral_condKernel_eq_measure_prod, ProbabilityTheory.Kernel.setLIntegral_rnDeriv_le, VitaliFamily.exists_measurable_supersets_limRatio, ProbabilityTheory.Kernel.iIndepSet_zero_right, Measure.instModuleIsTorsionFree, ae_map_iff_ae_trim, Measure.ae_eval_ne, Measure.AbsolutelyContinuous.instRefl, TendstoInMeasure.exists_seq_tendsto_ae', trim_comap_apply, llr_smul_left, MonotoneOn.ae_differentiableWithinAt, Measure.coe_zero, volume_sum_rpow_lt_one, condExpL2_const_inner, PMF.toMeasure_uniformOfFinset_apply, IsFundamentalDomain.measure_eq_tsum, Measure.singularPart_add, ProbabilityTheory.IsKolmogorovProcess.edist_eq_zero, ae_measure_preimage_add_right_lt_top, Submartingale.condExp_sub_nonneg, ProbabilityTheory.tilted_mul_apply_cgf', Measure.map_snd_prod, coeFn_fourierLp, ae_iff_measure_eq, Measure.singularPart_smul, self_mem_ae_restrict, ProbabilityTheory.Kernel.lintegral_restrict, IsHahnDecomposition.le_on, PMF.toMeasure_apply_eq_zero_iff, LipschitzWith.ae_differentiableAt_real, measureReal_restrict_applyβ', DominatedFinMeasAdditive.add_measure_right, Measure.infinitePi_pi_of_countable, IsFiniteMeasure.measure_univ_lt_top, ProbabilityTheory.Kernel.swap_apply', ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, measure_preimage_add, Measure.IsCondKernel.apply_of_ne_zero, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, Measure.comap_zero, lintegral_one, measure_preimage_fst_singleton_eq_sum, pdf.ofReal_toReal_ae_eq, ProbabilityTheory.Kernel.indepSets_singleton_iff, SimpleFunc.finMeasSupp_iff_support, mem_map_indicator_ae_iff_of_zero_notMem, AEFinStronglyMeasurable.exists_set_sigmaFinite, Subgroup.index_mul_measure, condExp_mul_of_stronglyMeasurable_left, Lp.simpleFunc.zero_toSimpleFunc, LinearMap.exists_map_addHaar_eq_smul_addHaar', ProbabilityTheory.ofReal_cdf, iInf_mul_le_setLIntegral, Orientation.measure_orthonormalBasis, measure_sigmaFiniteSetGE_ge, ProbabilityTheory.Kernel.coe_comap, Martingale.stoppedValue_ae_eq_condExp_of_le, Measure.toSphere_apply_univ', Measure.rnDeriv_smul_right_of_ne_top, IsOpen.measure_eq_zero_iff, IsOpen.ae_eq_zero_of_integral_contDiff_smul_eq_zero, Measure.sub_zero, Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, condExp_bot_ae_eq, NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, Measure.sum_coe_finset, tsum_meas_le_meas_iUnion_of_disjointβ, ProbabilityTheory.Kernel.integral_deterministic, Measure.InnerRegularCompactLTTop.smul, trim_add, MeasurePreserving.measure_preimage, AEEqFun.inv_toGerm, Content.measure_apply, ProbabilityTheory.Kernel.iIndepSets.ae_isProbabilityMeasure, Measure.addHaar_closedBall_eq_addHaar_ball, condExp_ae_eq_restrict_of_measurableSpace_eq_on, ProbabilityTheory.Kernel.comp_null, tilted_apply', IsFundamentalDomain.projection_respects_measure_apply, ContinuousLinearMap.coeFn_holder, Measure.haarMeasure_eq_iff, Integrable.prod_right_ae, eLpNorm_indicator_const, withDensity_apply, Measure.measurable_join, Measure.ext_prod_iff, ae_lt_top, hausdorffMeasure_of_lt_dimH, condExpL2_indicator_nonneg, measure_lt_top_of_isCompact_of_isMulLeftInvariant', OuterMeasure.toMeasure_top, Measure.Regular.zero, ProbabilityTheory.Kernel.swapLeft_apply, ProbabilityTheory.Kernel.fst_compProd_apply, ae_comp_linearMap_mem_iff, Measure.MutuallySingular.add_right_iff, ae_eq_of_integral_contDiff_smul_eq, BoundedContinuousFunction.lintegral_le_edist_mul, Measure.mkMetric_mono_smul, Measure.InnerRegularWRT.measurableSet_of_isOpen, ProbabilityTheory.deterministic_comp_posterior, PMF.toMeasure_apply_fintype, Measure.addHaar_closedBall', ae_eq_of_integral_smooth_smul_eq, Measure.restrict_inter_add_diff, measureReal_nnreal_smul_apply, unitInterval.volume_Iio, Real.volume_interval, ZSpan.fundamentalDomain_ae_parallelepiped, ProbabilityTheory.iIndepSets_singleton_iff, ProbabilityTheory.setLIntegral_toKernel_Iic, MemLp.exists_eLpNorm_indicator_compl_lt, ae_iff_prob_eq_one, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Lp.mul_meas_ge_le_pow_enorm, Measure.rnDeriv_le_one_iff_le, ProbabilityTheory.Kernel.IsProper.lintegral_mul, measure_unionβ, IsOpen.measure_pos_iff, Measure.ae_smul_measure_eq, Measure.piContent_eq_infinitePiNat, one_le_div_ae, ae_eq_zero_of_forall_setIntegral_isClosed_eq_zero, StieltjesFunction.measure_const, Measure.prod_smul_left, AEEqFun.coeFn_pair, Measure.toSphere_eq_zero_iff, withDensity_zero_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero_of_measurable, SignedMeasure.rnDeriv_add, ProbabilityTheory.Kernel.HasSubgaussianMGF.zero_measure, Measure.restrict_iUnion_le, AEEqFun.add_toGerm, ProbabilityTheory.Kernel.prod_apply_prod, ProbabilityTheory.Kernel.IsProper.inter_eq_indicator_mul, Measure.haveLebesgueDecompositionSMul', neg_llr, Measure.iSup_restrict_spanningSets_of_measurableSet, AEEqFun.coeFn_one, ProbabilityTheory.setBernoulli_eq_map, SimpleFunc.sum_range_measure_preimage_singleton, diracProba_toMeasure_apply_of_mem, pdf.ae_lt_top, ContinuousLinearMap.coeFn_compLp', forall_measure_preimage_mul_right_iff, measure_biUnionβ, PMF.toMeasure_map_apply, ProbabilityTheory.condExpKernel_apply_eq_condDistrib, PMF.toMeasure_apply_eq_tsum, Measure.bind_const, Real.volume_emetric_ball, ProbabilityTheory.uniformOn_eq_zero', ProbabilityTheory.integrable_stieltjesOfMeasurableRat, ProbabilityTheory.Kernel.lintegral_prod_id, Measure.OuterRegular.measure_closure_eq_of_isCompact, Conservative.frequently_ae_mem_and_frequently_image_mem, ProbabilityTheory.Kernel.singularPart_of_subset_mutuallySingularSetSlice, Measure.rnDeriv_add_right_of_mutuallySingular, AddContent.measureCaratheodory_eq, Iio_ae_eq_Iic, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet_ae_interior, SignedMeasure.rnDeriv_sub, Measure.addHaar_smul, PMF.toMeasure_apply_finset, Measure.InnerRegular.zero, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, ProbabilityTheory.posterior_comp, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, dirac_withDensity, Measure.instOuterMeasureClass, Real.map_volume_mul_left, FiniteMeasure.null_iff_toMeasure_null, ProbabilityTheory.Kernel.lintegral_id', Measure.InnerRegularWRT.exists_subset_lt_add, measure_mul_closure_one, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_condDistrib_prod_condDistrib, Measure.sum_extend_zero, Measure.addHaar_image_homothety, ProbabilityTheory.Kernel.iIndepFun_iff_measure_inter_preimage_eq_mul, Measure.toPMF_apply, Measure.measure_isHaarMeasure_eq_smul_of_isOpen, unitInterval.volume_Ioi, IsAddFundamentalDomain.measure_le_of_pairwise_disjoint, ProbabilityTheory.Kernel.integral_indicatorβ
|