NNReal 📖 | CompOp | 2271 math, 2 bridgemath: Delone.DeloneSet.mapBilipschitz_coveringRadius, range_cfcₙ_nnreal, SpectrumRestricts.le_nnreal_iff, NNReal.HolderConjugate.mul_eq_add, NNReal.summable_and_Lr_rpow_le_Lp_mul_Lq_tsum, MeasureTheory.FiniteMeasure.mass_map_le, PiLp.lipschitzWith_toLp, MeasureTheory.tendsto_integral_thickenedIndicator_of_isClosed, NNReal.tendsto_agmSequences_fst_agm, MeasureTheory.Measure.MutuallySingular.smul_nnreal, nnnorm_inv, NNReal.pow_arith_mean_le_arith_mean_pow, Seminorm.isBounded_const, PiLp.norm_toLp_const', NNReal.orderIsoIccZeroCoe_apply_coe_coe, NNReal.hasSum_lt, MeasureTheory.Measure.IsHaarMeasure.nnreal_smul, MeasureTheory.mulEquivHaarChar_smul_integral_map, NNReal.summable_coe, MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure, SpectrumRestricts.nnreal_of_nonneg, PiLp.nndist_eq_sum, Matrix.frobenius_nnnorm_mul, NNReal.summable_and_inner_le_Lp_mul_Lq_tsum, MeasureTheory.Measure.isAddInvariant_eq_smul_of_compactSpace, LipschitzWith.id, Complex.nnnorm_exp_I_mul_ofReal, NNReal.rpow_sub_intCast, ProbabilityTheory.gaussianReal_map_const_mul, List.nnnorm_prod, NNReal.toReal_lt, ODE.FunSpace.exists_contractingWith_iterate_next, NNReal.tsum_geometric, LipschitzWith.prodMk_right, Dilation.ratio_one, Real.toNNReal_lt_natCast', ENNReal.toNNReal_pow, NNReal.HolderTriple.inv_eq, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, NNReal.HolderTriple.one_div_nonneg', Orthonormal.nnnorm_eq_one, ENNReal.some_eq_coe', eq_zero_or_nnnorm_pos, IsPicardLindelof.of_contDiffAt_one, ENNReal.coe_eq_one, Topology.IsClosedEmbedding.continuousOn_comap_finiteMeasure, CFC.monotoneOn_one_sub_one_add_inv, thickenedIndicator_mono_infEDist, isCompact_setOf_finiteMeasure_mass_eq_compl_isCompact_le, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, MeasureTheory.integral_smul_nnreal_measure, LinearIsometry.nnnorm_toContinuousLinearMap, nnnorm_le_insert', NNReal.rpow_rpow_inv, nnnorm_le_nnnorm_add_nnnorm_div', 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MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply, parallelogram_law_with_nnnorm, PreTilt.valAux_eq, ApproximatesLinearOn.lipschitz, Commute.cfcₙ_nnreal, HolderOnWith.interpolate, AntilipschitzWith.mul_le_nndist, NNReal.mul_iSup_le, BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBot', nndist_self, MeasureTheory.llr_smul_nnreal_same, Real.toNNReal_mul, Fin.nndist_insertNth_insertNth, Seminorm.finset_sup_apply, NNReal.zero_rpow, NNReal.pow_antitone_exp, pi_nnnorm_le_iff, setIntegral_withDensity_eq_setIntegral_smul₀, LipschitzWith.mk_one, NumberField.mixedEmbedding.one_le_convexBodyLTFactor, thickenedIndicator_one_of_mem_closure, PadicComplex.valuation_extends, PadicComplex.charZero, MeasureTheory.addEquivAddHaarChar_pos, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, LipschitzWith.prod_snd, NNReal.coe_toRealHom, nndist_pi_le_iff, BoundedContinuousFunction.nnnorm_add_eq_max, PiLp.norm_toLp_one, IsUltrametricDist.nnnorm_tprod_le_of_forall_le, NNReal.rpow_lt_one, Real.toNNReal_le_toNNReal_iff', HolderWith.of_le, LinearIsometryEquiv.antilipschitz, HasSum.toNNReal, MeasureTheory.Measure.measure_isMulLeftInvariant_eq_smul_of_ne_top, PadicComplex.coe_eq, eventually_enorm_mfderivWithin_symm_extChartAt_lt, AEMeasurable.ennreal_toNNReal, MeasureTheory.smul_le_stoppedValue_hittingBtwn, ENNReal.ofNNReal_natCast_sub, LipschitzWith.holderWith, NNReal.exists_lt_of_strictMono, IsometryClass.lipschitz, unitInterval.toNNReal_continuous, EMetric.NonemptyCompacts.lipschitz_prod, Real.tendsto_toNNReal_atTop_iff, Complex.lipschitz_equivRealProd, nnnorm_cfcₙ_lt_iff, PadicComplex.norm_eq_norm, ContinuousLinearMap.nnnorm_def, QuasispectrumRestricts.nnreal_iff, Complex.nndist_self_conj, Pi.norm_def', CFC.nnnorm_sqrt, PMF.support_bernoulli, List.nnnorm_prod_le', nnnorm_nsmul_le, NNReal.canLift, NNReal.sqrt_le_iff_le_sq, HolderOnWith.comp, TopologicalSpace.Compacts.lipschitz_prod, nndist_eq_zero, NumberField.FinitePlace.norm_def', MeasureTheory.ProbabilityMeasure.exists_lt_measure_biUnion_of_isOpen, ENNReal.coe_finset_sum, NNReal.coe_sSup, ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFun, InformationTheory.klDiv_smul_right_eq_smul_left, Summable.countable_support_nnreal, ENNReal.coe_min, NNReal.sqrt_mul_lt_half_add_of_ne, NNReal.instTietzeExtension, MeasureTheory.ProbabilityMeasure.prod_prod, MeasureTheory.Measure.haveLebesgueDecompositionSMul, MeasureTheory.Lp.nnnorm_le_of_ae_bound, MeasureTheory.le_eLpNorm_of_bddBelow, IsGreatest.nnnorm_cfcₙ, ENNReal.isOpenEmbedding_coe, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, MeasureTheory.mulEquivHaarChar_symm, nnnorm_sum_le, NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv, ENNReal.tendsto_toNNReal_iff', NNReal.tendsto_dist_agmSequences_atTop_zero, NNReal.instSecondCountableTopology, Real.toNNReal_le_ofNat, MeasureTheory.Measure.coe_nnreal_smul_apply, ENNReal.summable_toNNReal_of_tsum_ne_top, MeasureTheory.FiniteMeasure.zero_testAgainstNN, ENNReal.smul_def, NNReal.limsInf_of_not_isCobounded, CFC.abs_nnrpow_two, NNReal.inner_le_Lp_mul_Lq_hasSum, instStarModuleNNRealOfReal, NNReal.rpow_add_rpow_le_add, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, ContinuousMap.toNNReal_neg_algebraMap, NNReal.rpow_intCast_mul, NNReal.coe_le_one, ENNReal.lt_iff_exists_add_pos_lt, ContinuousLinearMap.opNNNorm_le_iff, NumberField.HeightOneSpectrum.rankOne_hom'_def, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, NNReal.segment_eq_uIcc, NNReal.pow_rpow_inv_natCast, nnnorm_le_add_nnnorm_add, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_compProd, IsometryClass.antilipschitz, nnnorm_le_mul_nnnorm_add, AntilipschitzWith.id, ContinuousMap.coeNNRealReal_apply, CompactlySupportedContinuousMap.nnrealPart_smul_neg, nndist_midpoint_right, NNReal.div_lt_one_of_lt, NNReal.summable_sigma, ENNReal.toNNReal_sub, WithLp.prod_nnnorm_eq_add, nndist_smul₀, MeasureTheory.eLpNorm_smul_measure_of_ne_top', NNReal.orderIsoRpow_apply, MeasureTheory.Measure.rnDeriv_smul_right, ENNReal.iInf_ennreal, NNReal.agmSequences_zero, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, ContinuousLinearMap.ebound, cfcₙHom_nnreal_eq_restrict, MeasureTheory.Measure.haarScalarFactor_pos_of_isHaarMeasure, MeasureTheory.exists_upperSemicontinuous_le_lintegral_le, NNReal.tendsto_atTop_zero_of_summable, AntilipschitzWith.mul_le_dist, NNReal.agm_lt_max_of_ne, NNReal.rpow_natCast, nnnorm_le_nnnorm_add_nnnorm_sub, ContDiff.lipschitzWith_of_hasCompactSupport, ProbabilityTheory.gaussianReal_zero_var, Real.le_toNNReal_iff_coe_le, NNReal.pi_pos, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, NNReal.coe_add, SpectrumRestricts.nnreal_iff, MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass, Real.toNNReal_pow, Measurable.ennreal_toNNReal, PadicComplex.coe_natCast, MeasureTheory.Measure.haarScalarFactor_smul, MeasureTheory.Measure.OuterRegular.smul_nnreal, NNReal.not_summable_iff_tendsto_nat_atTop, NNReal.coe_iSup, IsUltrametricDist.nnnorm_pow_le, NNReal.sqrt_sq, EuclideanSpace.nndist_eq, NNReal.rpow_lt_rpow_iff_of_neg, Dilation.antilipschitz, NNReal.sqrt_pos, HolderWith.add, NNReal.summable_geometric, DilationEquiv.edist_eq', MeasureTheory.ProbabilityMeasure.range_toFiniteMeasure, Matrix.nnnorm_lt_iff, ContinuousLinearMap.exists_nonlinearRightInverse_of_surjective, ProbabilityTheory.HasSubgaussianMGF.const_mul, NumberField.mixedEmbedding.convexBodyLT_volume, NormedField.exists_lt_nnnorm_lt, instStarModuleNNRealReal, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, NormedField.exists_nnnorm_lt_one, NNReal.coe_div, NNReal.le_sqrt_iff_sq_le, Dilation.ratio_id, NNReal.sqrt_eq_rpow, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, ENNReal.toNNReal_sSup, Metric.exists_continuous_nnreal_forall_closedBall_subset, ENNReal.nhds_top', nnnorm_le_insert, NNReal.isBoundedSMul, PiLp.nnnorm_eq_of_L2, ENNReal.toNNReal_le_toNNReal, NNReal.half_le_self, MeasureTheory.MemLp.meas_ge_lt_top, NNReal.agm_le_agmSequences_snd, Real.toNNReal_add, NNReal.rpow_mul_intCast, ENNReal.toNNReal_mul_top, Continuous.cfc_nnreal', nndist_right_lineMap, UniformOnFun.lipschitzWith_one_ofFun_toFun, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, aemeasurable_coe_nnreal_real_iff, nndist_nnnorm_nnnorm_le_nnnorm_inv_mul, NNReal.HolderTriple.nonneg', ENNReal.tsum_toNNReal_eq, EMetric.exists_continuous_nnreal_forall_closedBall_subset, Similar.exists_nndist_eq, ENat.map_coe_nnreal, NNReal.sqrt_zero, WithLp.nndist_fst_le, MeasureTheory.ProbabilityMeasure.continuous_lintegral_boundedContinuousFunction, nnnorm_algebraMap_nnreal, NonUnitalStarAlgHom.nnnorm_apply_le, NNReal.young_inequality, NNReal.spectrum_nonempty, CFC.rpow_def, NNReal.map_coe_atTop, ENNReal.rpow_ofNNReal, ContinuousLinearMap.sSup_sphere_eq_nnnorm, ContinuousAlternatingMap.le_opNNNorm, NNReal.rpow_inv_lt_iff_of_pos, nndist_add_add_le, ContinuousMultilinearMap.le_of_opNNNorm_le, MeasureTheory.Lp.nnnorm_eq_zero_iff, LipschitzOnWith.sub, Real.toNNReal_lt_toNNReal_iff_of_nonneg, ENNReal.coe_zpow, NNReal.HolderTriple.left_pos, Complex.reCLM_nnnorm, IsometryEquiv.toDilationEquiv_ratio, Metric.coveringNumber_two_mul_le_externalCoveringNumber, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, Matrix.linfty_opNNNorm_mulVec, ContinuousLinearMap.exists_lt_apply_of_lt_opNNNorm, nndist_left_lineMap, CFC.rpow_algebraMap, Real.toNNReal_prod_of_nonneg, ediam_smul_le, NNReal.tsum_mul_right, NNReal.eventually_pow_one_div_le, ApproximatesLinearOn.norm_fderiv_sub_le, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, Dilation.ratio_mul, NNReal.rpow_zero_pos, Mathlib.Meta.NormNum.IsNat.nnreal_rpow_isNNRat, MeasureTheory.FiniteMeasure.continuous_testAgainstNN_eval, MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_comp, SpectrumRestricts.smul_of_nonneg, NNReal.rpow_lt_rpow_of_neg, CFC.nnrpow_one, NNReal.agmSequences_fst_le_agm, NNReal.iSup_eq_zero, ENNReal.coe_mem_upperBounds, NNReal.algebraMap_eq_coe, NNReal.natCast_iInf, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto, HolderOnWith.nndist_le_of_le, NNReal.image_coe_uIoc, NNReal.image_coe_Ico, ENNReal.measurable_toNNReal, NNReal.coe_rpow, NNReal.rpow_add_intCast', ENNReal.iSup_ne_top, MeasureTheory.uniformIntegrable_iff, FormalMultilinearSeries.nnnorm_changeOrigin_le, ENNReal.image_coe_uIoc, MeasureTheory.AEStronglyMeasurable.nnnorm, norm_algebraMap_nnreal, NNReal.instPosSMulStrictMono, similar_iff_exists_dist_eq, NNReal.dist_agmSequences_fst_snd, NNReal.HolderTriple.of_pos, NNReal.one_le_rpow, nnnorm_div, NNRealRMK.lintegral_rieszMeasure, nnnorm_one, MeasureTheory.addEquivAddHaarChar_smul_preimage, WithLp.prod_nndist_eq_of_L1, thickenedIndicator_zero, ENNReal.coe_max, NNReal.rpow_le_one_of_one_le_of_nonpos, lipschitzWith_sup_right, ProbabilityTheory.gaussianReal_map_continuousLinearMap, MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN, HolderWith.holderWith_zero_of_bounded, eq_one_or_nnnorm_pos, NNReal.rpow_lt_rpow, HasOuterApproxClosed.tendsto_apprSeq, DilationClass.edist_eq', FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, nnnorm_mul_le, LipschitzWith.of_edist_le, Hamming.nndist_eq_hammingDist, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, TopologicalSpace.Compacts.lipschitz_sup, BoxIntegral.IntegrationParams.hasBasis_toFilter, similar_iff_exists_nndist_eq, ENNReal.image_coe_Iic, SemilinearIsometryClass.lipschitz, NNReal.rpow_eq_pow, Matrix.frobenius_nnnorm_one, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', integral_withDensity_eq_integral_smul, NNReal.isSquare, MeasureTheory.FiniteMeasure.mass_prod, PiLp.nnnorm_toLp_one, ENNReal.zero_eq_coe, MeasureTheory.FiniteMeasure.testAgainstNN_const, thickenedIndicator_le_one, ENNReal.range_coe, ENNReal.instSMulPosMonoNNReal, NNReal.count_const_le_le_of_tsum_le, BoxIntegral.Prepartition.distortion_le_of_mem, NNReal.instContinuousMap.UniqueHom, MeasureTheory.FiniteMeasure.tendsto_iff_weakDual_tendsto, MeasureTheory.integrable_thickenedIndicator, NormedField.exists_nnnorm_lt, MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul, MeasureTheory.FiniteMeasure.tendsto_measure_iUnion_accumulate, MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul, ContinuousLinearMap.antilipschitz_of_isEmbedding, nnnorm_mul₃_le, rieszContentAux_image_nonempty, MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero, LipschitzWith.mul_end, Real.toNNReal_sum_of_nonneg, NNReal.coe_eq_zero, NNReal.strictConcaveOn_sqrt, Valued.integer.exists_norm_lt_one, NNReal.arith_mean_le_rpow_mean, MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn, MeasureTheory.mulEquivHaarChar_pos, WithZeroMulInt.toNNReal_pos, NNReal.sqrt_le_sqrt, ContinuousMap.toNNReal_algebraMap, ENNReal.csupr_ne_top, PiLp.antilipschitzWith_toLp, InnerProductSpace.nnnorm_rankOne, MeasureTheory.JordanDecomposition.real_smul_nonneg, pi_nnnorm_lt_iff, antilipschitzWith_iff_exists_mul_le_norm', ENNReal.coe_sSup, ENNReal.natCast_le_ofNNReal, NNReal.image_coe_uIcc, MeasureTheory.JordanDecomposition.real_smul_neg, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, Seminorm.ball_smul, NNReal.isGreatest_Lp, Real.one_lt_toNNReal, NNReal.rpow_inv_rpow, antilipschitzWith_mul_right, CFC.abs_nnrpow, LinearMap.exists_antilipschitzWith, NNReal.isCoboundedUnder_le_toReal, ContinuousMap.continuous_toNNReal, NNReal.coe_prod, MeasureTheory.Measure.smul_measure_isAddInvariant_le_of_isCompact_closure, CompactlySupportedContinuousMap.exists_add_of_le, nndist_smul_le, BoundedContinuousFunction.lintegral_lt_top_of_nnreal, SimpleGraph.binomialRandom_apply, nnnorm_cfcₙ_nnreal_lt, CFC.nnrpow_sqrt_two, LipschitzWith.dist_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, MeasureTheory.FiniteMeasure.tendsto_iff_forall_lintegral_tendsto, nndist_inv_inv₀, CStarAlgebra.nnnorm_le_iff_of_nonneg, NumberField.HeightOneSpectrum.adicAbv_def, NNReal.natCast_natAbs, nnnorm_smul, NNReal.continuous_coe, List.nnnorm_prod_le, CompactlySupportedContinuousMap.coe_toRealLinearMap, NNReal.bddBelow_coe, MeasureTheory.condExpIndSMul_empty, Similar.exists_dist_eq, nnnorm_le_mul_nnnorm_add', NNReal.HolderConjugate.inv_add_inv_eq_one, Real.toNNReal_div, ENNReal.toNNReal_add, BoxIntegral.Box.nndist_le_distortion_mul, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, NormedField.denseRange_nnnorm, MeasureTheory.lpNorm_smul_measure_of_ne_zero, LipschitzWith.of_le_add, MeasureTheory.SimpleFunc.nnnorm_approxOn_le, NNReal.rpow_inv_rpow_eq_iff, lipschitzOnWith_cfc_fun_of_subset, eventually_nnnorm_sub_lt, NNReal.rpow_sub_natCast, NNReal.isEmbedding_coe, unitInterval.toNNReal_zero, cfc_real_eq_nnreal, ENNReal.iSup_coe_lt_top, Real.toNNReal_le_one, NNReal.closedBall_zero_eq_Icc, Hamming.nnnorm_eq_hammingNorm, StarAlgHom.realContinuousMapOfNNReal_apply, ENNReal.toNNReal_div, AffineIsometry.lipschitz, NNReal.lt_iff_exists_rat_btwn, NNReal.rpow_sub, ProbabilityTheory.setBernoulli_apply', indiscreteTopology_iff_forall_nnnorm_eq_zero, NNReal.rpow_sub', BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion_top, NNReal.hasLipschitzAdd, MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize, Valued.integer.norm_irreducible_lt_one, MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure, MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul', NNReal.HolderTriple.inv_sub_inv_eq_inv, Dilation.edist_eq', Real.toNNReal_ofNat, Metric.uniformContinuous_infNndist_pt, NNReal.tendsto_agmSequences_snd_agm, NNReal.coe_multiset_prod, Real.toNNReal_monotone, NNReal.rpow_neg_one, similar_iff_exists_edist_eq, MeasureTheory.FiniteMeasure.pi_pi, Real.nnabs_of_nonneg, WithZeroMulInt.toNNReal_lt_one_iff, infEDist_smul₀, Dilation.nndist_eq, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, MeasureTheory.ProbabilityMeasure.pi_pi, nndist_le_pi_nndist, nnnorm_zpow_le_mul_norm, NNReal.rpow_le_rpow, MeasureTheory.mulEquivHaarChar_smul_map, ENNReal.coe_tsum, LipschitzWith.prod_fst, BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion, LipschitzWith.pow_end, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, NNReal.comap_coe_atTop, MeasureTheory.ProbabilityMeasure.apply_mono, NNReal.rpow_sum_le_const_mul_sum_rpow, PiLp.nndist_apply_le, holderWith_zero_iff, BoundedContinuousFunction.nndist_set_exists, MeasureTheory.Measure.addModularCharacterFun_map_zero, PseudoMetricSpace.dist_ofPreNNDist, MeasureTheory.distribHaarChar_apply, MeasureTheory.Content.sup_disjoint', LipschitzWith.projIcc, BoundedContinuousFunction.Lp_nnnorm_le, NNReal.eq_rpow_inv_iff, dist_le_coe, NNReal.iSup_mul_iSup_le, CFC.posPart_algebraMap_nnreal, NNReal.hasSum_real_toNNReal_of_nonneg, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, ENNReal.instIsScalarTowerNNReal, lipschitzWith_thickenedIndicator, MeasureTheory.FiniteMeasure.map_fst_prod, isCompact_setOf_finiteMeasure_mass_le_compl_isCompact_le, coe_mem_spectrum_real_of_nonneg, antilipschitzWith_iff_le_mul_nndist, CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestricts, FormalMultilinearSeries.compAlongComposition_nnnorm, TopologicalSpace.NonemptyCompacts.lipschitz_prod, MeasureTheory.FiniteMeasure.pos_mono, NNReal.rpow_le_rpow_of_exponent_ge, IsGreatest.nnnorm_cfc, Metric.packingNumber_two_mul_le_externalCoveringNumber, MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto, NNReal.rpow_mul, PiLp.nnnorm_toLp_const', MeasureTheory.FiniteMeasure.testAgainstNN_coe_eq, CFC.nnrpow_map_pi, UpperHalfPlane.volume_def, selfAdjoint.nnnorm_pow_two_pow, ModP.preVal_mul, Real.nnnorm_nnratCast, NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def, SemilinearMapClass.nnbound_of_continuous, NNReal.rpow_add_natCast', Metric.IsCover.image_lipschitz_of_surjective, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, setIntegral_withDensity_eq_setIntegral_smul₀', AEMeasurable.real_toNNReal, nndist_triangle_right, ENNReal.coe_rpow_of_nonneg, NNReal.one_le_coe, MeasureTheory.Measure.hausdorffMeasure_smul₀, Dilation.ratioHom_apply, Real.toNNReal_le_toNNReal_iff, Finset.nnnorm_prod_le', NNReal.sqrt_eq_iff_eq_sq, ENNReal.tendsto_coe_toNNReal, SpectrumRestricts.nnreal_lt_iff, NNReal.HolderTriple.inv_nonneg, NNReal.coe_zero, exists_spanning_measurableSet_le, NNReal.summable_nat_add, ENNReal.lt_iff_exists_coe, MeasureTheory.FiniteMeasure.coeFn_def, BoxIntegral.TaggedPrepartition.distortion_disjUnion, NNReal.addLeftMono, LipschitzWith.list_prod, MeasureTheory.exists_simpleFunc_forall_lintegral_sub_lt_of_pos, ENNReal.le_coe_iff, LipschitzOnWith.prodMk, ProbabilityTheory.gaussianReal_map_linearMap, indiscreteTopology_iff_forall_nnnorm_eq_zero', NNReal.range_coe, ENNReal.coe_lt_coe, nnnorm_multiset_sum_le, Valuation.RankOne.exists_val_lt, ENNReal.toNNReal_one, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, NNReal.isClosedEmbedding_coe, CompactlySupportedContinuousMap.toRealLinearMap_apply, Matrix.l2_opNNNorm_mulVec, MeasureTheory.SMul.sigmaFinite, PiLp.nnnorm_apply_le, HasStrictFDerivAt.exists_lipschitzOnWith, NNReal.map_coe_nhdsGT, MeasureTheory.SimpleFunc.exists_lt_lintegral_simpleFunc_of_lt_lintegral, MeasureTheory.ProbabilityMeasure.toNNReal_measureReal_eq_coeFn, MeasureTheory.measureUnivNNReal_eq_zero, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_innerRegular, LipschitzWith.comp_lipschitzOnWith, Complex.antilipschitz_equivRealProd, RCLike.nnnorm_nnratCast, ENNReal.prod_coe_rpow, TensorProduct.nnnorm_tmul, AntilipschitzWith.le_mul_nnnorm', NNReal.rpow_lt_rpow_of_exponent_gt, NNReal.smulCommClass_left, BoxIntegral.Prepartition.distortion_biUnionTagged, NNReal.holderConjugate_one_div, NNReal.bddAbove_range_agmSequences_fst, NNReal.image_coe_Iio, CFC.posPart_smul, NNReal.isBoundedUnder_ge_toReal, ContinuousWithinAt.nnnorm, continuousOn_cfc_nnreal, measurable_real_toNNReal, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, MeasureTheory.FiniteMeasure.zero_testAgainstNN_apply, lipschitzWith_one_norm', nnnorm_algebraMap, nnnorm_pow, MeasureTheory.ProbabilityMeasure.coeFn_empty, Real.coe_nnabs, NNReal.agm_mul_distrib, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, uniformContinuous_nndist, ENNReal.continuous_coe_iff, MeasureTheory.mulEquivHaarChar_refl, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, ProbabilityTheory.map_pi_eq_stdGaussian, cfc_nnreal_eq_real, nnnorm_apply_le_nnnorm_cfcₙ, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, Seminorm.bound_of_continuous, NNReal.agm_eq_ciSup, MeasureTheory.Measure.rnDeriv_smul_left', MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul', Polynomial.cauchyBound_C, ENNReal.toNNReal_iSup, nnnorm_pow_le, BoxIntegral.TaggedPrepartition.distortion_le_of_mem, nndist_single_single, NNReal.rpow_lt_rpow_of_exponent_lt, ENNReal.toNNReal_pos, AntilipschitzWith.mul_div_lipschitzWith, ContinuousLinearMap.opNNNorm_le_bound, Filter.IsIncreasingApproximateUnit.eventually_nnnorm, Prod.nnnorm_def, NNReal.summable_mul_rpow_of_Lp_Lq, Real.toNNReal_le_natCast, MeasureTheory.ProbabilityMeasure.coeFn_def, Complex.ofRealCLM_nnnorm, nnHolderNorm_zero, WithZeroMulInt.toNNReal_neg_apply, ContinuousWithinAt.nnnorm', tendsto_real_toNNReal, CFC.nnrpow_def, ENNReal.exists_ne_top, LipschitzOnWith.mk_one, ProbabilityTheory.HasSubgaussianMGF.fun_zero, HolderOnWith.of_le_of_le, PreTilt.valAux_zero, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, MeasureTheory.UniformIntegrable.spec', ENNReal.coe_le_coe, ENNReal.coe_inv', MeasureTheory.FiniteMeasure.coeFn_zero, NNReal.HolderTriple.inv_inv_add_inv, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regular, NNReal.tendsto_of_antitone, similar_iff_exists_pairwise_dist_eq, TopologicalSpace.Closeds.lipschitz_sup, Metric.coveringNumber_zero, CFC.nnrpow_inv_nnrpow, QuasispectrumRestricts.le_nnreal_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.add, WithLp.prod_nnnorm_eq_of_L2, MeasureTheory.ProbabilityMeasure.toFiniteMeasure_apply, ENNReal.orderIsoIicCoe_symm_apply_coe, ENNReal.tendsto_toNNReal, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_lintegral, Valuation.RankOne.strictMono, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, FormalMultilinearSeries.radius_inv_eq_limsup, NNReal.instStarOrderedRing, nndist_left_midpoint, nnnorm_mul_le', MeasureTheory.measure_of_cont_bdd_of_tendsto_filter_indicator, WithLp.prod_nnnorm_eq_of_L1, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, NNReal.sSup_of_not_bddAbove, NNReal.lipschitzWith_sub, nnnorm_pos', NNReal.instIsTopologicalSemiring, NNReal.inv_rpow, nnHolderNorm_const, NNReal.rpow_right_inj, CFC.sqrt_eq_nnrpow, lipschitzWith_circleMap, MeasureTheory.ProbabilityMeasure.map_apply_of_aemeasurable, CompactlySupportedContinuousMap.toReal_apply, PositiveLinearMap.exists_norm_apply_le, IsUltrametricDist.nnnorm_mul_le_max, LipschitzWith.min, IsSelfAdjoint.nnnorm_mul_self, NNReal.continuousAt_rpow, NNReal.agmSequences_fst_lt_snd_of_ne, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, MeasureTheory.measureUnivNNReal_pos, PiLp.lipschitzWith_ofLp, HasOuterApproxClosed.measure_le_lintegral, MeasureTheory.SimpleFunc.sum_eapproxDiff, Real.lipschitzWith_sin, ENNReal.coe_range_mem_nhds, indicator_le_thickenedIndicator, Isometry.toDilation_ratio, ContinuousMap.nnnorm_lt_iff, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, LipschitzWith.prodMk, NNReal.tsum_eq_add_tsum_ite, SpectrumRestricts.nnreal_le_iff, NNReal.rpow_ofNat, Real.toNNReal_inv, NNReal.bot_eq_zero, FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendsto, NNReal.sqrt_mul, PadicAlgCl.instUniformContinuousConstSMulPadic, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.Measure.modularCharacterFun_map_mul, isClosedMap_nndist, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, lipschitzOnWith_cfc_fun, MeasureTheory.Measure.toSignedMeasure_smul, NNReal.HolderConjugate.two_two, WithLp.prod_antilipschitzWith_toLp, IsUltrametricDist.nnnorm_add_eq_max_of_nnnorm_ne_nnnorm, Real.ofNat_lt_toNNReal, SchauderBasis.bddAbove_range_nnnorm_proj, CFC.abs_nnrpow_two_mul, NNReal.rpow_arith_mean_le_arith_mean_rpow, Continuous.cfc_nnreal_of_mem_nhdsSet, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_lintegral, HolderWith.interpolate_const, NNReal.iSup_pow_of_ne_zero, NNReal.le_add_nndist, NNReal.one_lt_rpow_of_pos_of_lt_one_of_neg, MeasureTheory.StronglyMeasurable.real_toNNReal, ENNReal.le_toNNReal_of_coe_le, NNReal.zero_rpow_def, MeasureTheory.Measure.addHaarScalarFactor_eq_mul, BoundedContinuousFunction.nnrealPart_coeFn_eq, PadicAlgCl.valuation_p, ENNReal.coe_one, ENNReal.nhds_coe, MeasureTheory.hausdorffMeasure_lineMap_image, PadicComplex.valuation_p, Continuous.cfcₙ_nnreal, isCompact_setOf_finiteMeasure_eq_of_compactSpace, ContinuousLinearMap.nnnorm_holder_apply_apply_le, AffineMap.lipschitzWith_of_finiteDimensional, ENat.toENNRealOrderEmbedding_apply, MeasureTheory.ProbabilityMeasure.tendsto_measure_iUnion_accumulate, ContinuousLinearMap.isClosed_range_iff_antilipschitz_of_injective, NNReal.instIsOrderBornology, ENNReal.toNNReal_strict_mono, tendsto_real_toNNReal_atTop, NNReal.nnrpow_def, MeasureTheory.FiniteMeasure.testAgainstNN_add, infEdist_smul₀, NumberField.mixedEmbedding.adjust_f, MeasureTheory.FiniteMeasure.apply_iUnion_le, NNReal.add_rpow_le_rpow_add, LipschitzMul.lipschitz_mul, NNReal.sqrt_eq_zero, NNReal.rpow_two, SemilinearMapClass.ebound_of_continuous, Real.comap_toNNReal_atTop, PadicComplex.norm_extends', MeasureTheory.FiniteMeasure.apply_mono, WithZeroMulInt.toNNReal_le_one_iff, nnnorm_surjective, NNReal.sub_def, nndist_midpoint_left, MeasureTheory.L1.nnnorm_integral_le, MeasureTheory.FiniteMeasure.tendsto_zero_testAgainstNN_of_tendsto_zero_mass, ProbabilityTheory.HasCondSubgaussianMGF.zero, MeasureTheory.FiniteMeasure.instContinuousSMulNNReal, NNReal.coe_lt_one, Valued.integer.norm_le_one, Module.Basis.exists_opNNNorm_le, PreTilt.valAux_mul, MeasureTheory.ProbabilityMeasure.apply_le_one, NNReal.mul_self_sqrt, Mathlib.Meta.NormNum.IsNNRat.nnreal_rpow_isNNRat, Filter.Tendsto.nndist, MeasureTheory.distribHaarChar_eq_of_measure_smul_eq_mul, NNReal.agmSequences_min_max, isCompact_setOf_finiteMeasure_le_of_compactSpace, ContinuousAt.cfcₙ_nnreal, ProbabilityTheory.gaussianReal_conv_gaussianReal, ENNReal.ofNNReal_le_natCast, DilationEquiv.ratio_inv, Real.toNNReal_pos, ENNReal.coe_essSup, NNReal.ContinuousMap.canLift, NNReal.strictMono_rpow_of_pos, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul, PadicComplex.isNonarchimedean, NNReal.lt_rpow_inv_iff, NNReal.agmSequences_fst_monotone, ENNReal.coe_eq_zero, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbvDef, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isOpen, ContinuousLinearMap.isLeast_opNNNorm, ContinuousMap.nnnorm_smul_const, ENNReal.coe_add, nnnorm_eq_zero', Seminorm.const_isBounded, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, MeasureTheory.Measure.rnDeriv_smul_same, MeasureTheory.FiniteMeasure.testAgainstNN_mono, MeasureTheory.FiniteMeasure.restrict_eq_zero_iff, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, LipschitzOnWith.extend_finite_dimension, CStarAlgebra.nnnorm_sub_mul_self_le, DilationEquiv.ratio_zpow, MeasureTheory.exists_lt_lintegral_simpleFunc_of_lt_lintegral, ModP.preVal_mk, nndist_midpoint_midpoint_le', Real.toNNReal_lt_iff_lt_coe, WithLp.prod_lipschitzWith_ofLp, ModP.v_p_lt_preVal, Real.toNNReal_lt_toNNReal_iff, NNReal.rpow_natCast_mul, ContinuousMap.toNNReal_one, MeasureTheory.Lp.lipschitzWith_pos_part, ENNReal.image_coe_uIoo, MeasureTheory.FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure, Real.toNNReal_one, coe_comp_nnnorm', PiNat.exists_lipschitz_retraction_of_isClosed, measure_le_lintegral_thickenedIndicator, IsStrictlyPositive.nnrpow, NNReal.exists_pow_lt_of_lt_one, Real.toNNReal_div', NNReal.geom_mean_le_arith_mean4_weighted, NNReal.mul_finset_sup, ProbabilityTheory.gaussianReal_mul_const, ENNReal.coe_rpow_of_ne_zero, NNReal.tendsto_rpow_atTop, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, Delone.DeloneSet.mapBilipschitz_packingRadius, NNReal.tsum_comp_le_tsum_of_inj, Dilation.ratio_pow, nndist_center_homothety, one_le_thickenedIndicator_apply', dimH_eq_iInf, LipschitzWith.vadd, NNReal.rpow_inv_eq_iff, ENat.floor_coe, ENNReal.coe_le_one_iff, Delone.DeloneSet.packingRadius_pos, Real.toNNReal_eq_natCast, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure, NNReal.HolderTriple.lt, NNReal.rpow_le_one, ENNReal.nnreal_smul_lt_top_iff, cfcₙ_tsub, Pi.nnnorm_def', CFC.rpow_neg_one_eq_cfc_inv, NNReal.summable_nat_add_iff, ContinuousLinearMap.opNNNorm_le_bound', NNReal.instContinuousInv₀, NNReal.rpow_add_natCast, Matrix.l2_opNNNorm_mul, nndist_vsub_vsub_le, MeasureTheory.addEquivAddHaarChar_eq_one_of_compactSpace, NNReal.coe_natCast, Pi.sum_nnnorm_apply_le_nnnorm, PiLp.nnnorm_eq_ciSup, Polynomial.cauchyBound_one, nndist_nnnorm_nnnorm_le_nnnorm_neg_add, NNReal.geom_mean_le_arith_mean2_weighted, NNReal.coe_tsum_of_nonneg, NNReal.image_coe_Ioc, NNReal.mul_sup, pi_nnnorm_le_iff', Matrix.nnnorm_entry_le_entrywise_sup_nnnorm, ContinuousWithinAt.cfcₙ_nnreal, nnnorm_cfc_le_iff, ENNReal.iSup_ennreal, MeasureTheory.smul_le_stoppedValue_hitting, MeasureTheory.Measure.addModularCharacterFun_map_add, CStarAlgebra.nnnorm_le_one_iff_of_nonneg, WithLp.prod_nndist_eq_add, ContinuousLinearMap.opNNNorm_le_of_unit_nnnorm, NNReal.rpow_inv_le_iff_of_pos, NNReal.coe_sum, MeasureTheory.Measure.isMulInvariant_eq_smul_of_compactSpace, Metric.exists_continuous_nnreal_forall_closedEBall_subset, MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Real.nnnorm_mul_toNNReal, ContinuousMap.nnnorm_lt_iff_of_nonempty, lp.lipschitzWith_one_eval, ENNReal.coe_two, CFC.continuousOn_nnrpow, nnnorm_prod_le_of_le, MeasureTheory.FiniteMeasure.tendsto_lintegral_nn_of_le_const, ValuativeRel.RankLeOneStruct.strictMono, AntilipschitzWith.mul_lipschitzWith, Dilation.ratio_pos, nnnorm_le_pi_nnnorm, MeasureTheory.eLpNormLESNormFDerivOneConst_def, QuasispectrumRestricts.lt_nnreal_iff, CompactlySupportedContinuousMap.integralLinearMap_apply, nndist_mul_mul_le, ProbabilityTheory.gaussianReal_map_div_const, NormedField.exists_one_lt_nnnorm, nndist_triangle, NNReal.rpow_eq_left_iff, NNReal.rpow_le_self_of_le_one, Real.toNNReal_add_le, NNReal.agm_eq_agm_gm_am, MeasureTheory.FiniteMeasure.mass_comap_le, AntilipschitzWith.le_mul_nndist, NNReal.tendsto_sum_nat_add, ENNReal.toNNReal_natCast, nnnorm_indicator_eq_indicator_nnnorm, NumberField.canonicalEmbedding.nnnorm_eq, NNReal.rpow_lt_rpow_iff, MeasureTheory.memL1_smul_of_L1_withDensity, ENNReal.coe_finset_prod, MeasureTheory.llr_smul_nnreal_left, ProbabilityTheory.gaussianPDF_zero_var, range_cfcₙ_nnreal_eq_image_cfcₙ_real, NNReal.list_prod_map_rpow', IsSelfAdjoint.sq_spectrumRestricts, NNReal.rpow_inv_le_iff, Filter.Tendsto.cfcₙ_nnreal, ProbabilityTheory.IdentDistrib.nnnorm, NNReal.le_gm_and_am_le, UpperHalfPlane.volume_eq_lintegral, AntilipschitzWith.pos, lipschitzOnWith_cfcₙ_fun, Real.nnnorm_two, NNReal.isBoundedUnder_le_toReal, ENNReal.coe_finset_sup, NNReal.continuous_sqrt, CFC.nnrpow_zero, ContinuousMultilinearMap.isLeast_opNNNorm, NNReal.HolderTriple.one_div_nonneg, congruent_iff_pairwise_nndist_eq, Real.toNNReal_mul_nnnorm, LipschitzWith.uncurry, Mathlib.Meta.NormNum.IsNat.nnreal_rpow_eq_nnreal_pow, NNReal.image_coe_Ici, CFC.nnrpow_sqrt, MeasureTheory.JordanDecomposition.smul_posPart, HolderOnWith.interpolate_const, NNReal.HolderConjugate.one_sub_inv_inv, SemilinearIsometryClass.antilipschitz, nndist_lineMap_right, edist_smul₀, ENNReal.toNNReal_iInf, MeasureTheory.FiniteMeasure.testAgainstNN_zero, IsUnit.cfcNNRpow, Pi.norm_def, NNReal.min_le_agm, Set.OrdConnected.image_coe_nnreal_real, NNReal.le_iInf_mul_iInf, thickenedIndicator_tendsto_indicator_closure, WithLp.prod_lipschitzWith_toLp, NNReal.rpow_eq_zero, MeasureTheory.FiniteMeasure.mono_null, MeasureTheory.ProbabilityMeasure.continuous_lintegral_continuousMap, uniformity_basis_edist_nnreal_le, nndist_triangle_left, MeasureTheory.FiniteMeasure.prod_apply, ENNReal.one_eq_coe, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure, NNReal.one_le_rpow_of_pos_of_le_one_of_nonpos, NNReal.rpow_add', IsUltrametricDist.nnnorm_sum_le_of_forall_le, NNReal.isCoboundedUnder_ge_toReal, ENNReal.toNNReal_rpow, NNReal.coe_min, MeasureTheory.mul_le_addHaar_image_of_lt_det, MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply, Real.toNNReal_lt_one, ContinuousOn.cfc_nnreal, NNReal.iSup_div, nnnorm_cfcₙ_nnreal_lt_iff, NNReal.coe_nnqsmul, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePos, ContinuousLinearMap.nonlinearRightInverseOfSurjective_def, NNReal.exists_pos_sum_of_countable, ENNReal.coe_ofNNRealHom, Pi.sum_nnnorm_apply_le_nnnorm', HolderOnWith.holderOnWith_zero_of_bounded, rieszContentAux_sup_le, LipschitzWith.add, UniformOnFun.lipschitzWith_eval, HolderWith.comp_holderOnWith, MeasureTheory.Measure.nnreal_smul_coe_apply, Real.toNNReal_eq_zero, NNReal.rpow_add, NNReal.summable_comp_injective, NNReal.hasSum_geometric, NNReal.one_lt_rpow, NNReal.isOpen_Ico_zero, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, MeasureTheory.euclideanHausdorffMeasure_homothety_image, RCLike.lipschitzWith_re, Seminorm.closedBall_smul, MeasureTheory.FiniteMeasure.coeFn_smul, ENNReal.smulCommClass_left, nnnorm_cfc_nnreal_lt, NumberField.FinitePlace.norm_def_int, BoundedContinuousFunction.nnnorm_sum_eq_sup, MeasureTheory.euclideanHausdorffMeasure_homothety_preimage, NNReal.sub_div, MeasureTheory.L1.nnnorm_Integral_le_one, NNReal.coe_two, NNReal.coe_nsmul, MeasureTheory.Measure.addHaarScalarFactor_smul_smul, MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg, Units.nnnorm_pos, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, NNReal.HolderTriple.pos', ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, NNReal.le_rpow_inv_iff, edist_lt_coe, Tactic.NormNum.isNNRat_nnrealSqrt_of_isNNRat, enorm_lt_coe, Real.toNNReal_mono, MeasureTheory.hausdorffMeasure_homothety_image, NNReal.summable_of_sum_range_le, NNReal.rpow_inv_rpow_self, MeasureTheory.mulEquivHaarChar_trans, IsUltrametricDist.nnnorm_tsum_le_of_forall_le, Set.InvOn.one_sub_one_add_inv, ApproximatesLinearOn.antilipschitz, NNReal.HolderTriple.holderConjugate_div_div, NNReal.rpow_add_rpow_le, NNReal.HolderConjugate.conjugate_eq, cfcₙ_real_eq_nnreal, Convex.exists_nhdsWithin_lipschitzOnWith_of_hasFDerivWithinAt, ENNReal.lt_iff_exists_nnreal_btwn, ProbabilityTheory.gaussianReal_map_mul_const, ENNReal.iSup_coe_eq_top, BoundedContinuousFunction.nndist_coe_le_nndist, nnnorm_cfc_nnreal_le, similar_iff_exists_pairwise_edist_eq, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, MeasureTheory.Measure.smul_measure_isMulInvariant_le_of_isCompact_closure, nnnorm_inner_le_nnnorm, NNReal.sqrt_eq_one, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, cfc_nnreal_le_iff, NNReal.sqrt_pos_of_pos, ENNReal.coe_inv_two, Continuous.cfc_nnreal, nnnorm_pow_le_mul_norm, InnerProductGeometry.angle_eq_angle_add_angle_iff, MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePos, ENNReal.coe_lt_natCast, Measurable.nnnorm, nnnorm_cfc_nnreal_le_iff, MeasureTheory.IsFiniteMeasureOnCompacts.smul_nnreal, BoxIntegral.TaggedPrepartition.distortion_filter_le, NNReal.coe_ofScientific, ENNReal.ofNNReal_liminf, TopologicalSpace.Closeds.lipschitz_prod, Real.toNNReal_le_toNNReal, ENNReal.tendsto_toNNReal_iff, ENNReal.coe_pos, HasOuterApproxClosed.apprSeq_apply_eq_one, MeasureTheory.integrable_withDensity_iff_integrable_smul, PadicComplex.instIsScalarTowerPadicPadicAlgCl, PiLp.antilipschitzWith_ofLp, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet, ConvexBody.smul_le_of_le, ENNReal.exists_pos_sum_of_countable, Real.lipschitzWith_one_mulExpNegMulSq, MeasureTheory.FiniteMeasure.restrict_apply, Nonneg.instContinuousFunctionalCalculus, ContinuousLinearMap.antilipschitz_of_injective_of_isClosed_range, AntilipschitzWith.subtype_coe, nndist_pi_const_le, Congruent.pairwise_nndist_eq, IsPrimitiveRoot.nnnorm_eq_one, BoundedContinuousFunction.nndist_eq_iSup, nndist_pi_def, NNReal.rpow_sub_one, IsUltrametricDist.nnnorm_sum_eq_sup_of_pairwise_ne, MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero, Valued.integer.coe_span_singleton_eq_closedBall, NNReal.nndist_eq, Complex.conjCLE_nnorm, NNReal.natCast_iSup, pi_nnnorm_const_le', Real.toNNReal_lt_ofNat, IsUltrametricDist.nnnorm_prod_eq_sup_of_pairwise_ne, NNReal.rpow_inv_le_iff_of_neg, Measurable.real_toNNReal, NNReal.rpow_one_sub', NNReal.rpow_intCast, ENNReal.coe_zero, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, HasFTaylorSeriesUpToOn.exists_lipschitzOnWith, SchwartzMap.eLpNorm_le_seminorm, NNReal.continuousOn_rpow_const, ENNReal.coe_mul, NNReal.rpow_left_injective, LipschitzWith.sub, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, NNReal.hasSum_iff_tendsto_nat, LipschitzWith.vsub, ENNReal.tendsto_coe, MeasureTheory.MeasuredSets.lipschitzWith_measureReal, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, ENNReal.toNNReal_mono, nnnorm_zero, Complex.nnnorm_ofNat, Set.OrdConnected.preimage_coe_nnreal_ennreal, LipschitzWith.iterate, MeasureTheory.FiniteMeasure.restrict_mass, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_lintegral, ContinuousMapZero.toContinuousMapHom_toNNReal, WithLp.nnnorm_fst_le, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply, MeasureTheory.FiniteMeasure.coeFn_add, NNReal.spectralRadius_mem_spectrum, NNReal.coe_inv, CFC.spectrum_rpow, ProbabilityTheory.gaussianReal_add_gaussianReal_of_indepFun, ContinuousMultilinearMap.opNNNorm_prod, LipschitzWith.dist_right, BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition, Complex.nnnorm_nnratCast, CFC.nnrpow_inv_eq, NNReal.smul_def, MeasureTheory.nnnorm_indicatorConstLp_le, enorm_le_coe, NNReal.summable_Lp_add, IsUltrametricDist.nnnorm_nsmul_le, NNReal.agmSequences_monotone_and_antitone, ProbabilityTheory.HasSubgaussianMGF.sub_of_indepFun, MeasureTheory.Measure.map_right_mul_eq_modularCharacterFun_smul, NNReal.rpow_add_le_mul_rpow_add_rpow, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, cfcHom_nnreal_eq_restrict, PadicComplex.norm_eq_norm', rieszContentAux_mono, MeasureTheory.AEStronglyMeasurable.real_toNNReal, MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_filter_of_le_const, ENNReal.exists_pos_tsum_mul_lt_of_countable, MeasureTheory.addEquivAddHaarChar_smul_map, NNReal.sum_mul_le_sqrt_mul_sqrt, HasOuterApproxClosed.tendsto_lintegral_apprSeq, NNReal.smulCommClass_right, NNReal.rpow_le_rpow_of_nonpos, NNReal.lt_inv_iff_mul_lt, NNReal.rpow_add_intCast, LipschitzOnWith.add, upperHemicontinuous_spectrum_nnreal, Real.one_le_toNNReal, ProbabilityTheory.cauchyPDFReal_def', ContinuousOn.nnnorm, CFC.nnrpow_nnrpow, NNReal.le_rpow_inv_iff_of_neg, MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN, CompletelyRegularSpace.exists_BCNN, MeasureTheory.JordanDecomposition.coe_smul, eventually_enorm_mfderiv_extChartAt_lt, NNReal.rpow_eq_rpow_iff, HolderOnWith.exists_holderOnWith_of_le, ContinuousOn.cfcₙ_nnreal', NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, NNReal.coe_sub_def, ENNReal.range_coe', MeasureTheory.addHaar_image_le_mul_of_det_lt, Polynomial.one_le_cauchyBound, NNReal.tsum_lt_tsum, Real.toNNReal_of_nonpos, MeasureTheory.ProbabilityMeasure.apply_iUnion_le, nnnorm_smul_le, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, NNReal.continuousAt_rpow_const, BoxIntegral.Prepartition.distortion_disjUnion, Real.nndist_eq, CompactlySupportedContinuousMap.toReal_add, MeasureTheory.isMulLeftInvariant_smul_nnreal, ContinuousOn.nnnorm', NumberField.mixedEmbedding.convexBodyLT'_volume, NNReal.ball_zero_eq_Ico', NNReal.tsum_eq_toNNReal_tsum, thickenedIndicator_subset, range_cfc_nnreal, ProbabilityTheory.Kernel.HasSubgaussianMGF.zero, ContinuousLinearMap.le_opNNNorm, nnnorm_cfc_le, NNReal.holderConjugate_iff_eq_conjExponent, ContinuousLinearMap.nonlinearRightInverseOfSurjective_nnnorm_pos, LinearIsometry.antilipschitz, NNReal.HolderTriple.right_pos, Metric.coveringNumber_subset_le, MeasureTheory.lintegral_eq_nnreal, LipschitzWith.prodMk_left, ENNReal.image_coe_Iio, NNReal.one_le_sqrt, Unitization.nnreal_cfcₙ_eq_cfc_inr, range_nnnorm, ENNReal.ofNNReal_sub_natCast, NNReal.lt_rpow_inv_iff_of_neg, NNReal.div_le_of_le_mul, ContinuousMap.realToNNReal_apply, MeasureTheory.instIsProbabilityMeasureHAddMeasureHSMulNNRealToNNRealSymm, NNReal.Lp_add_le_hasSum, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, NNReal.le_mul_iInf, hasConstantSpeedOnWith_zero_iff, ProbabilityTheory.gaussianPDFReal_inv_mul, NNReal.HolderConjugate.inv_inv, NNReal.coe_expect, nnnorm_le_nnnorm_add_nnnorm_div, ENNReal.coe_inv_le, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, NNReal.rpow_add_one, nnnorm_apply_le_nnnorm_cfc, ENNReal.coe_nnratCast, setIntegral_withDensity_eq_setIntegral_smul, BoxIntegral.Prepartition.distortion_biUnion, BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm, NNReal.HolderTriple.inv_add_inv_eq_inv, IsometricContinuousFunctionalCalculus.spectrum_le, MeasureTheory.FiniteMeasure.map_apply, nnnorm_pow_le', InformationTheory.toReal_klDiv_smul_right_eq_smul_left, Valued.integer.norm_unit, Real.le_toNNReal_iff_coe_le', NNReal.rpow_lt_one_of_one_lt_of_neg, BoundedContinuousFunction.nnnorm_coe_le_nnnorm, SchauderBasis.nnnorm_proj_le_nnnormProjBound, thickenedIndicator_apply, dist_lt_coe, MeasureTheory.Measure.modularCharacterFun_map_one, ENNReal.continuousOn_toNNReal, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, nndist_nnnorm_nnnorm_le', NNReal.half_lt_self, nnnorm_eq_zero, MeasureTheory.Measure.measure_isAddLeftInvariant_eq_vadd_of_ne_top, CFC.abs_algebraMap_nnreal, CFC.zero_nnrpow, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, NNReal.inner_le_weight_mul_Lp, NNReal.rpow_add_one', lipschitzWith_negPart, NNReal.le_toNNReal_of_coe_le, MeasureTheory.FiniteMeasure.testAgainstNN_one, ENNReal.iInf_ne_top, Real.lipschitzWith_toNNReal, BoundedContinuousFunction.nnnorm_le, upperHemicontinuous_quasispectrum_nnreal, ProbabilityTheory.HasSubgaussianMGF.add, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, MeasureTheory.SimpleFunc.exists_le_lowerSemicontinuous_lintegral_ge, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbvDef, PadicAlgCl.valuation_def, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, edist_le_coe, NNReal.lt_rpow_inv_iff_of_pos, NNReal.rpow_le_rpow_iff_of_neg, MeasureTheory.Measure.mul_addHaarScalarFactor_smul, CompactlySupportedContinuousMap.toNNRealLinear_apply, NNReal.geom_mean_le_arith_mean_weighted, BoxIntegral.Prepartition.distortion_bot, Set.OrdConnected.image_real_toNNReal, NNReal.le_inv_iff_mul_le, AntilipschitzWith.le_mul_nnnorm, nndist_midpoint_midpoint_le, WithLp.prod_nndist_eq_sup, NNReal.image_coe_Iic, ContinuousLinearMap.opNNNorm_mul, NNReal.Lr_le_Lp_mul_Lq, CFC.nnnorm_rpow, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, MeasureTheory.FiniteMeasure.smul_apply, Delone.DeloneSet.mapBilipschitz_trans, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, MeasureTheory.ProbabilityMeasure.apply_union_le, WithLp.prod_nnnorm_eq_sup, MeasureTheory.FiniteMeasure.measureReal_eq_coe_coeFn, BoundedContinuousFunction.nnnorm_const_le, CFC.nnrpow_le_nnrpow, IsPiSystem.tendsto_probabilityMeasure_biUnion, MemHolder.nnHolderNorm_nsmul, PiLp.norm_toLp_const, NNReal.instMeasurableSMul₂ENNReal, nnnorm_tsum_le, nnnorm_fderiv_norm_rpow_le, ProbabilityTheory.gaussianPDFReal_zero_var, NNReal.orderIsoIccZeroCoe_symm_apply_coe, HasStrictFDerivAt.approximates_deriv_on_open_nhds, TrivSqZeroExt.nnnorm_def, similar_iff_exists_pairwise_nndist_eq, MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_le_const, MeasureTheory.Measure.isMulLeftInvariant_eq_smul, NNReal.mul_eq_mul_left, PadicAlgCl.valuation_coe, LipschitzWith.max, ENNReal.coe_rpow_def, lipschitzWith_one_nnnorm, InformationTheory.toReal_klDiv_smul_right, ContinuousAlternatingMap.isLeast_opNNNorm, ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNorm, PadicComplex.coe_zero, NNReal.HolderTriple.one_div_eq, MeasureTheory.SimpleFunc.map_coe_nnreal_restrict, apply_le_nnnorm_cfc_nnreal, MeasureTheory.FiniteMeasure.mk_apply, setOf_riemannianEDist_lt_subset_nhds, eventually_riemannianEDist_le_edist_extChartAt, CFC.nnrpow_eq_pow, NNReal.segment_eq_Icc, ENNReal.coe_comp_toNNReal_comp, MeasureTheory.tendsto_lintegral_thickenedIndicator_of_isClosed, NNReal.coe_mono, MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz, NNReal.exists_le_hasSum_of_le, WithLp.nnnorm_snd_le, Similar.exists_edist_eq, NNReal.div_le_of_le_mul', ContinuousMap.toNNReal_apply, lipschitzOnWith_cfcₙ_fun_of_subset, range_cfc_nnreal_eq_image_cfc_real, uniformContinuous_nnnorm, NNReal.instContinuousSMulOfReal, NNReal.rpow_rpow_inv_eq_iff, ENNReal.continuousAt_coe_iff, MeasureTheory.VAddInvariantMeasure.vadd_nnreal, LipschitzWith.nnorm_le_mul', CFC.nnrpow_eq_nnrpow_pi, ENNReal.tsum_coe_ne_top_iff_summable, Complex.nnnorm_natCast, Valued.integer.exists_nnnorm_lt_one, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, NNReal.inv_lt_inv, BoxIntegral.Prepartition.distortion_le_iff, Complex.nndist_conj_self, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, NNReal.instOrderTopology, NNReal.agmSequences_fst_le_snd, DilationEquivClass.edist_eq', MeasureTheory.Measure.InnerRegular.smul_nnreal, ContinuousLinearMap.nndist_le_opNNNorm, DilationEquiv.ratio_trans, NNRealRMK.le_rieszMeasure_of_tsupport_subset, Polynomial.cauchyBound_zero, MeasureTheory.FiniteMeasure.zero_mass, Real.toNNReal_le_toNNReal_iff_of_pos, Summable.toNNReal, ENNReal.toNNReal_apply_of_tsum_ne_top, Filter.Tendsto.nnnorm', MeasureTheory.JordanDecomposition.smul_negPart, LipschitzWith.eval, Matrix.linfty_opNNNorm_mul, Real.toNNReal_zpow, thickenedIndicator_mono_infEdist, Real.toNNReal_add_toNNReal, AntilipschitzWith.comp, Real.nnabs_coe, Isometry.lipschitz, MeasureTheory.isAddRightInvariant_smul_nnreal, NNReal.image_coe_Ioi, MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto, range_cfcₙ_nnreal_subset, MemHolder.nnHolderNorm_smul, NNReal.nhds_zero, DilationEquiv.ratio_refl, MeasureTheory.SMulInvariantMeasure.smul_nnreal, MeasureTheory.mulEquivHaarChar_smul_preimage, CFC.nnrpow_three, Convex.lipschitz_gauge, Valuation.RankLeOne.exists_val_lt, ContinuousMap.nnnorm_add_eq_max, LipschitzWith.mul, NNReal.HolderConjugate.one_sub_inv, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, StarAlgHom.realContinuousMapOfNNReal_injective, Real.natCastle_toNNReal', NNReal.instProperSpace, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, SeminormedAddCommGroup.lipschitzWith_sub, antilipschitzWith_mul_left, NormedField.v_eq_valuation, RCLike.nnnorm_two, ENNReal.toNNReal_prod, NNReal.summable_one_div_rpow, NNReal.monotone_nnrpow_const, LipschitzWith.nndist_le, Nonneg.instNonUnitalContinuousFunctionalCalculus, ContinuousMap.nnnorm_eq_iSup_nnnorm, WithZeroMulInt.toNNReal_eq_one_iff, NNReal.nnnorm_eq_self, NNReal.rpow_neg, ENNReal.coe_sub, ContinuousLinearMap.opNNNorm_comp_le, NNReal.rpow_add_le_add_rpow, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, PreTilt.valAux_add, LipschitzOnWith.zero_iff, MemHolder.nnHolderNorm_add_le, NNReal.rpow_sub_one', Metric.isBounded_iff_nndist, NNReal.mul_lt_of_lt_div, MeasureTheory.ProbabilityMeasure.tendsto_measure_of_isClopen_of_tendsto, convex_setOf_holderWith, NNReal.orderIsoRpow_symm_eq, NNReal.coe_pow, Dilation.ratio_comp, ENNReal.toNNReal_lt_toNNReal, NNReal.agmSequences_fst_lt_agm_of_pos_of_ne, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, ModP.preVal_zero, MeasureTheory.ProbabilityMeasure.map_apply, exists_lt_rieszContentAux_add_pos, ContinuousMap.nndist_eq_iSup, ApproximatesLinearOn.closedBall_subset_target, MeasureTheory.tendstoInMeasure_iff_tendsto_toNNReal, ProbabilityTheory.HasCondSubgaussianMGF.fun_zero, nnnorm_one', ProbabilityTheory.cauchyPDFReal_scale_zero, NNReal.limsSup_of_not_isBounded, ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGF, MeasureTheory.JordanDecomposition.real_smul_posPart_neg, NNReal.Lp_add_le_tsum', MeasureTheory.FiniteMeasure.normalize_testAgainstNN, NNReal.rpow_sub_natCast', Metric.frontier_cthickening_disjoint, HolderOnWith.comp_holderWith, Real.toNNReal_abs, MeasureTheory.Measure.exists_positive_of_not_mutuallySingular, Submodule.lipschitzWith_starProjection, NNReal.agm_eq_agm_agmSequences_fst_agmSequences_snd, Int.nnnorm_coe_units, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_regular, NNReal.continuous_rpow_const, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, measurable_coe_nnreal_real, ProbabilityTheory.HasSubgaussianMGF.add_of_indepFun, ediam_smul₀, PiLp.nnnorm_eq_of_L1, NNReal.continuous_nnrpow_const, MeasureTheory.withDensitySMulLI_apply, MeasureTheory.Measure.addHaar_nnreal_smul, NonUnitalIsometricContinuousFunctionalCalculus.quasispectrum_le, BoundedContinuousFunction.lipschitz_compContinuous, Pi.nnnorm_def, NNReal.isUniformEmbedding_coe, Prod.nnnorm_mk', NNReal.bddAbove_natCast_image_iff, Metric.continuous_infNndist_pt, uniformContinuous_nnnorm', NNReal.addLeftReflectLT, NNReal.HolderConjugate.inv_one_sub_inv, NNReal.sum_add_tsum_nat_add, NNReal.HolderConjugate.div_conj_eq_sub_one, NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one, NNReal.HolderTriple.inv_pos', NNReal.instContinuousSub, ENNReal.cinfi_ne_top, MeasureTheory.Content.mono', NNReal.finset_prod_rpow, ENNReal.none_eq_top, ProbabilityTheory.cauchyPDF_scale_zero, Unitization.nnnorm_eq_sup, Seminorm.bound_of_shell_sup, holderWith_id, NNReal.coe_iInf, continuous_real_toNNReal, ContinuousLinearMap.nnnorm_smulRight_apply, LipschitzOnWith.of_le_add, NNReal.coe_mulIndicator, MeasureTheory.StronglyMeasurable.nnnorm, PadicComplex.RankOne.hom_eq_embedding, ContinuousMultilinearMap.opNNNorm_le_iff, Continuous.nndist, TopologicalSpace.NonemptyCompacts.lipschitz_sup, BoundedContinuousFunction.nnnorm_coeFn_eq, NNReal.image_coe_Ioo, NNReal.rpow_eq_rpow_right_iff, MeasureTheory.FiniteMeasure.map_smul, MeasureTheory.FiniteMeasure.prod_apply_symm, BoundedContinuousFunction.nnnorm_sub_eq_max, BoundedContinuousFunction.toReal_lintegral_coe_eq_integral, Complex.nnnorm_exp_ofReal_mul_I, NNReal.indicator_summable, GromovHausdorff.toGHSpace_lipschitz, NNRat.instContinuousSMulNNReal, nnnorm_multiset_prod_le, NNReal.HolderTriple.pos, NNReal.rpow_inv_lt_iff, NNReal.inv_le, Seminorm.finset_sup_smul, quasispectrum.isCompact_nnreal, ENNReal.orderIsoIicCoe_apply_coe, LipschitzWith.comp, MeasureTheory.FiniteMeasure.coeFn_mk, dist_pi_def, nnnorm_commutator_sub_one_le, MeasureTheory.ProbabilityMeasure.mk_apply, Seminorm.isBounded_sup, CFC.sqrt_eq_cfc, InformationTheory.toReal_klDiv_smul_same, ENNReal.coe_pow, NNReal.sup_mul, AEMeasurable.nnnorm, PMF.bernoulli_apply, MeasureTheory.addEquivAddHaarChar_smul_eq_comap, MeasureTheory.FiniteMeasure.continuous_lintegral_continuousMap, NNReal.summable_rpow_inv, ContDiffOn.exists_lipschitzOnWith, NNReal.coe_lt_coe, NNReal.rpow_eq_zero_iff, Real.toNNReal_zero, WithZeroMulInt.toNNReal_strictMono, Valued.toNormedField.norm_def, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, NNReal.toReal_le, QuasispectrumRestricts.nnreal_of_nonneg, nnnorm_cfcₙ_le_iff, IsUltrametricDist.nnnorm_intCast_le_one, MeasureTheory.Measure.modularCharacterFun_pos, PreTilt.valAux_one, NNReal.HolderTriple.all_pos, MeasureTheory.measureUnivNNReal_zero, Similar.exists_pairwise_dist_eq, instTrivialStarNNReal, Filter.Tendsto.cfc_nnreal, NNReal.rpow_arith_mean_le_arith_mean2_rpow, NNReal.limsup_of_not_isBoundedUnder, CompactlySupportedContinuousMap.toReal_smul, zero_eq_nndist, Convex.lipschitzWith_gauge, norm_cfcₙ_one_sub_one_add_inv_lt_one, PadicComplex.norm_extends, ConcaveOn.exists_lipschitzOnWith_of_isBounded, NNReal.monotone_rpow_of_nonneg, NNReal.hasMeasurablePow, continuousOn_cfcₙ_nnreal, MeasureTheory.mulEquivHaarChar_smul_eq_comap, NNReal.exists_mem_Ico_zpow, Continuous.nnnorm, Valuation.norm_def, ODE.FunSpace.apply_of_zero, ENNReal.tendsto_nhds_coe_iff, instBoundedSubNNReal, Valued.integer.mem_iff, MeasureTheory.FiniteMeasure.prod_prod, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous, NNReal.tsum_strict_mono, NNReal.iSup_empty, continuous_nnnorm, nnnorm_cfc_lt_iff, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_innerRegular, MeasureTheory.JordanDecomposition.real_smul_negPart_neg, IsUltrametricDist.nnnorm_tprod_le, FormalMultilinearSeries.summable_nnnorm_mul_pow, NNReal.borelSpace, spectrum.isCompact_nnreal, RCLike.lipschitzWith_ofReal, NNReal.Lr_rpow_le_Lp_mul_Lq_tsum, ContinuousLinearMap.opNNNorm_le_of_lipschitz, Int.abs_le_floor_nnreal_iff, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, AlternatingMap.measure_def, Metric.boundedSpace_iff_nndist, nnnormHom_apply, Seminorm.bound_of_shell_smul, MeasureTheory.eLpNormEssSup_lt_top_iff_isBoundedUnder, MeasureTheory.distribHaarChar_eq_div, ConvexOn.exists_lipschitzOnWith_of_isBounded, nndist_lineMap_lineMap, Irreducible.maximalIdeal_eq_closedBall, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, Isometry.antilipschitz, CFC.sqrt_nnrpow_two, Metric.lipschitz_infDist_pt, MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closure, Real.toNNReal_coe_nat, Int.nnnorm_natCast, NNReal.coe_multiset_sum, NNReal.mul_iSup, UnconditionalSchauderBasis.bddAbove_range_nnnorm_proj, Complex.imCLM_nnnorm, NNReal.coe_image, Finset.nnnorm_sum_le_sup_nnnorm, IsUltrametricDist.nnnorm_div_eq_max_of_nnnorm_div_ne_nnnorm_div, MeasureTheory.Measure.haarScalarFactor_smul_smul, Submodule.lipschitzWith_orthogonalProjection, MeasureTheory.Measure.rnDeriv_smul_left, MeasureTheory.UniformIntegrable.spec, MeasureTheory.Measure.haarScalarFactor_self, HasOuterApproxClosed.indicator_le_apprSeq, NNReal.sqrt_one, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, NNReal.inner_le_Lp_mul_Lq_tsum', ENNReal.coe_le_iff, Real.lipschitzWith_cos, BoundedContinuousFunction.measurable_coe_ennreal_comp, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, NNReal.Lp_add_le, CFC.sqrt_nnrpow, Metric.lipschitz_infDist, RCLike.nnnorm_nnqsmul, nnnorm_commutator_units_sub_one_le, Dilation.ratio_comp', NNReal.rpow_one_add', Set.OrdConnected.preimage_real_toNNReal, MeasureTheory.distribHaarChar_mul, NNReal.HolderTriple.one_div_add_one_div, cfcₙ_nnreal_eq_real, CFC.sqrt_algebraMap, NNReal.coe_pos, Valued.integer.isUnit_iff_norm_eq_one, holderOnWith_one, ENNReal.one_lt_coe_iff, BoundedContinuousFunction.nndist_eq, EMetric.Closeds.lipschitz_sup, NNReal.HolderTriple.inv_pos, sub_mem_posTangentConeAt_of_openSegment_subset, CompactlySupportedContinuousMap.nnrealPart_apply, NNReal.hasSum_strict_mono, IsUltrametricDist.nnnorm_natCast_le_one, PMF.mem_support_bernoulli_iff, NNReal.liminf_of_not_isCoboundedUnder, ContinuousLinearMap.opNNNorm_subsingleton, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, cfc_tsub, ContinuousLinearMap.IsPositive.spectrumRestricts, MeasureTheory.FiniteMeasure.apply_le_mass, CFC.nnrpow_eq_cfcₙ_real, ENNReal.smul_toNNReal, StieltjesFunction.measure_smul, Set.OrdConnected.preimage_coe_nnreal_real, AffineIsometryEquiv.lipschitz, MeasureTheory.FiniteMeasure.continuous_mass, coe_lt_enorm, Real.nnnorm_natCast, BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate, ENNReal.coe_mono, NNReal.continuousOn_rpow_const_compl_zero, Mathlib.Meta.Positivity.nnabs_pos_of_pos, NNReal.measurable_of_tendsto, NNReal.sqrt_le_one, HolderWith.nnholderNorm_le, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, ENNReal.image_coe_Ici, HolderOnWith.of_le, MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuous, nnnorm_sum_le_of_le, NNReal.coe_injective, MeasureTheory.ProbabilityMeasure.testAgainstNN_lipschitz, NNReal.ball_zero_eq_Ico, ENNReal.coe_strictMono, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, Real.toNNReal_le_iff_le_coe, nnnorm_sub_mul_le, ModP.v_p_lt_val, NNReal.coeNNRealReal_zero, LinearIsometryEquiv.lipschitz, WithZeroMulInt.toNNReal_pos_apply, ENNReal.image_coe_Ioi, NNReal.mk_natCast, NNReal.sInf_empty, spectrum.instCompactSpaceNNReal, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, MeasureTheory.SimpleFunc.exists_upperSemicontinuous_le_lintegral_le, MeasureTheory.Measure.Regular.smul_nnreal, Real.nnreal_trichotomy, NNReal.summable_of_le, IsUltrametricDist.nnnorm_zpow_le, NNReal.finset_sup_mul, NNReal.mul_iInf, NNReal.isometry_coe, NNReal.toReal_limsup, MeasureTheory.addEquivAddHaarChar_refl, NNReal.coe_mul, NNReal.summable_schlomilch_iff, MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval, nnnorm_cfc_nnreal_lt_iff, MeasureTheory.isLocallyFiniteMeasureSMulNNReal, ENNReal.toNNReal_mul, ENNReal.toNNReal_lt_of_lt_coe, Inseparable.nndist_eq_zero, Metric.inseparable_iff_nndist, coe_comp_nnnorm, CompactlySupportedContinuousMap.nnrealPart_smul_pos, nnnorm_le_nnnorm_add_nnnorm_sub', NNReal.min_lt_agm_of_pos_of_ne, NNReal.iInf_mul, MeasureTheory.ProbabilityMeasure.coeFn_toFiniteMeasure, UnconditionalSchauderBasis.nnnorm_proj_le_nnnormProjBound, MeasureTheory.ProbabilityMeasure.measureReal_eq_coe_coeFn, Real.toNNReal_lt_natCast, NNReal.geom_mean_le_arith_mean3_weighted, NNReal.tendsto_coe, MeasureTheory.isFiniteMeasureSMulNNReal, MeasureTheory.Integrable.smul_measure_nnreal, measurable_nndist, Real.nnreal_dichotomy, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, NNReal.inv_le_of_le_mul, NNReal.HolderTriple.inv_nonneg', NNReal.agmSequences_snd_antitone, CFC.nnrpow_eq_nnrpow_prod, spectrum.le_nnnorm_of_mem, Metric.lipschitz_infDist_set, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, Commute.cfc_nnreal, ContinuousMap.toNNReal_neg_one, Int.toNat_add_toNat_neg_eq_nnnorm, NNReal.rpow_zero, IndiscreteTopology.nnnorm_eq_zero', NNReal.summable_iff_not_tendsto_nat_atTop, NormedField.denselyOrdered_range_nnnorm, signedDist_eq_dist_iff_vsub_mem_span, thickenedIndicator_one, NNReal.exists_nat_pos_inv_lt, CFC.nnrpow_nnrpow_inv, LipschitzOnWith.holderOnWith, PiLp.nnnorm_eq_sum, Metric.packingNumber_zero, Unitization.antilipschitzWith_addEquiv, ENNReal.natCast_lt_coe, unitInterval.toNNReal_symm_add_toNNReal, nndist_pi_lt_iff, NNReal.iInf_empty, nnnorm_mul, NNReal.one_rpow, nndist_homothety_center, measurable_infNndist, BoundedContinuousFunction.lipschitz_eval_const, BoxIntegral.TaggedPrepartition.distortion_le_iff, Real.nnabs_pos, MeasureTheory.Measure.InnerRegularCompactLTTop.smul_nnreal, MeasureTheory.mulEquivHaarChar_eq_one_of_compactSpace, MeasureTheory.Measure.addModularCharacterFun_pos, Polynomial.cauchyBound_X_add_C, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, NNReal.agm_pos, MonotoneOn.nnnorm_cfc, convex_setOf_holderOnWith, MeasureTheory.FiniteMeasure.isEmbedding_toWeakDualBCNN, ContinuousLinearMap.nnnorm_id, PreTilt.map_eq_zero, NNReal.rpow_le_rpow_of_exponent_le, Matrix.frobenius_nnnorm_def, NNReal.summable_mul_of_Lp_Lq, LinearMap.mem_span_iff_bound, MeasureTheory.addEquivAddHaarChar_symm, ContinuousOn.cfcₙ_nnreal, MeasureTheory.Measure.IsEverywherePos.smul_measure_nnreal, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, CFC.nnrpow_eq_rpow, SpectrumRestricts.nnreal_iff_spectralRadius_le, NNReal.HolderTriple.one_div_pos, NNReal.sqrt_div, ENNReal.coe_nsmul, Matrix.nnnorm_le_iff, MeasureTheory.Measure.haveLebesgueDecompositionSMulRight, MeasureTheory.ProbabilityMeasure.tendsto_measure_of_null_frontier_of_tendsto, NNReal.dist_eq, MeasureTheory.FiniteMeasure.testAgainstNN_smul, MeasureTheory.FiniteMeasure.mass_zero_iff, NNReal.tendsto_coe_atTop, ENNReal.image_coe_Ioo, NNReal.coe_one, Real.nnnorm_rpow_of_nonneg, NNReal.tsum_mul_left, Irreducible.maximalIdeal_pow_eq_closedBall_pow, ENNReal.continuous_coe, ENNReal.toNNReal_sum, ENNReal.some_eq_coe, ENNReal.coe_div_le, MemHolder.nnHolderNorm_eq_zero, NNReal.le_iInf_add_iInf, MeasureTheory.SimpleFunc.tsum_eapproxDiff, ContinuousLinearEquiv.nnnorm_symm_pos, NNReal.tendsto_coe', continuous_nnnorm', Complex.nnnorm_I, Finset.nnnorm_prod_le_sup_nnnorm, pi_nnnorm_const_le, Finset.nnnorm_prod_le, MeasureTheory.Measure.IsAddHaarMeasure.nnreal_smul, NNReal.instIsStrictOrderedModule, UniformContinuous.nndist, EuclideanSpace.nnnorm_eq, NNReal.nhds_zero_basis, NNReal.instContinuousMapZero.UniqueHom, RCLike.nnnorm_natCast, IsUnifLocDoublingMeasure.one_le_scalingConstantOf, MeasureTheory.Measure.mul_haarScalarFactor_smul, NNReal.coe_mulSingle, ContinuousMapZero.toNNReal_neg_smul, NNReal.tsum_le_of_sum_range_le, IsUltrametricDist.nnnorm_mul_eq_max_of_nnnorm_ne_nnnorm, HolderOnWith.nndist_le, continuousOn_cfc_nnreal_setProd, LipschitzOnWith.comp, CStarRing.nnnorm_self_mul_star, ContinuousAt.nnnorm, MeasureTheory.exists_upperSemicontinuous_le_integral_le, Prod.nnnorm_def', MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_measurableSet, AffineIsometryEquiv.antilipschitz, Real.toNNReal_eq_one, ContinuousLinearMap.nnbound, Polynomial.cauchyBound_X_sub_C, NNReal.rpow_mul_natCast, NNReal.agmSequences_succ', CFC.nnrpow_nonneg, uniformity_basis_edist_nnreal, NNReal.one_lt_coe, CStarAlgebra.nonneg_TFAE, nndist_nnnorm_nnnorm_le, Module.Basis.opNNNorm_le, MeasureTheory.Measure.toSphereBallBound_pos, ProbabilityTheory.HasSubgaussianMGF.zero, HolderOnWith.exists_holderOnWith_of_le', ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, tsum_of_nnnorm_bounded, CStarAlgebra.nnnorm_le_nnnorm_of_nonneg_of_le, NNReal.hasSum_coe, NNReal.closedBall_zero_eq_Icc', BoundedContinuousFunction.lipschitz_evalx, Real.coe_sqrt, ENNReal.one_le_coe_iff, NNReal.hasSum_nat_add_iff, LinearMap.antilipschitz_of_comap_nhds_le, NNReal.nndist_zero_eq_val', MeasureTheory.lpNorm_smul_measure_of_ne_top, AffineIsometry.antilipschitz, NNReal.div_rpow, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_lintegral, ContinuousAlternatingMap.opNNNorm_le_iff, ContinuousMultilinearMap.nnnorm_smulRight, Real.tendsto_toNNReal_atTop, ENNReal.hasSum_coe, NNReal.inner_le_Lp_mul_Lq_tsum, LipschitzWith.const, MeasureTheory.addEquivAddHaarChar_trans, NNReal.instSMulPosStrictMono, AEMeasurable.nnreal_tsum, nnnorm_prod_le, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, NNReal.tendsto_tsum_compl_atTop_zero, NNReal.summable_condensed_iff, lipschitzWith_one_nnnorm', nnnorm_prod, NNReal.rpow_inv_natCast_pow, MeasureTheory.exists_eLpNorm_indicator_le, MeasureTheory.ProbabilityMeasure.coeFn_univ, ENat.ceil_coe, NNReal.sum_sqrt_mul_sqrt_le, NNReal.mulLeftMono, ModP.preVal_add, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, NNRealRMK.integral_rieszMeasure, NNReal.HolderConjugate.sub_one_pos, MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg, IndiscreteTopology.nnnorm_eq_zero, CFC.negPart_smul, CompactlySupportedContinuousMap.monotone_of_nnreal, PadicComplex.nnnorm_extends', Matrix.l2_opNNNorm_conjTranspose_mul_self, ContinuousMapZero.toNNReal_smul, ProbabilityTheory.gaussianReal_div_const, Dilation.ratio_of_trivial, TensorProduct.nndist_tmul_le, instBoundedMulNNReal, lipschitzExtensionConstant_pos, NNReal.agm_zero_left, ProbabilityTheory.gaussianPDFReal_mul, NNReal.coe_tsum, NNReal.coe_list_sum, ModP.preVal_eq_zero, CFC.isUnit_nnrpow_iff, NNReal.sqrt_mul_le_half_add, Real.map_toNNReal_atTop, lipschitzWith_max, NNReal.rpow_add_of_nonneg, NNReal.rpow_self_rpow_inv, MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀, NNReal.agm_zero_right, MeasureTheory.isMulRightInvariant_smul_nnreal, Real.lt_toNNReal_iff_coe_lt, NNReal.rpow_one, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, NNReal.Lr_rpow_le_Lp_mul_Lq, NormedField.valuation_apply, Unitization.lipschitzWith_addEquiv, NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv, IsUltrametricDist.nnnorm_sub_eq_max_of_nnnorm_sub_ne_nnnorm_sub, MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimate, NumberField.FinitePlace.norm_embedding', RCLike.nnnorm_nsmul, Real.toNNReal_rpow_of_nonneg, MeasureTheory.ProbabilityMeasure.null_iff_toMeasure_null, NNReal.rpow_left_surjective, MeasureTheory.isAddLeftInvariant_smul_nnreal, NNReal.agm_eq_ciInf, MeasureTheory.ProbabilityMeasure.prod_apply_symm, NNReal.exists, MeasureTheory.Measure.map_right_add_eq_addModularCharacterFun_vadd, ProbabilityTheory.HasSubgaussianMGF.sum_of_hasCondSubgaussianMGF, MeasureTheory.Measure.addHaarScalarFactor_pos_of_isAddHaarMeasure, NNReal.rpow_of_add_eq, ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNorm, NNReal.HolderConjugate.inv_add_inv_ennreal, ENNReal.image_coe_Ico, NumberField.mixedEmbedding.one_le_convexBodyLT'Factor, NNReal.coe_zpow, Delone.DeloneSet.mapBilipschitz_refl, Matrix.linfty_opNNNorm_replicateRow, MeasureTheory.Measure.haarScalarFactor_eq_mul, Valued.integer.norm_coe_unit, DilationEquiv.ratio_symm, MeasureTheory.hausdorffMeasure_homothety_preimage, Valuation.RankOne.hom_eq_zero_iff, ENNReal.image_coe_Icc, integral_withDensity_eq_integral_smul₀, NNReal.toReal_liminf, MeasureTheory.tendsto_lintegral_nn_filter_of_le_const, ContinuousAt.cfc_nnreal, Filter.Tendsto.nnrpow, parallelogram_law_with_nnnorm_mul, NNReal.HolderConjugate.sub_one_mul_conj, ENNReal.toNNReal_sInf, NNReal.list_prod_map_rpow, Set.OrdConnected.image_coe_nnreal_ennreal, HolderWith.smul, MeasureTheory.FiniteMeasure.map_snd_prod, ENNReal.instMeasurableSMulNNReal, nndist_right_midpoint, PiLp.nnnorm_toLp_const, Valuation.RankOne.restrict_RankOne_hom_eq, exists_continuous_add_one_of_isCompact_nnreal, Measurable.nndist, NNReal.mul_rpow, MeasureTheory.eLpNorm_smul_measure_of_ne_zero', lipschitzWith_posPart, ENNReal.coe_iInf, nnnorm_sub_mul_le', quasispectrum.instCompactSpaceNNReal, Polynomial.cauchyBound_X, NNReal.multiset_prod_map_rpow, MeasureTheory.OuterMeasure.mkMetric_nnreal_smul, SpectrumRestricts.lt_nnreal_iff, Filter.Tendsto.nnnorm, NNReal.rpow_le_rpow_iff, rieszContentAux_union, nnnorm_sub_le, NNReal.HolderTriple.nonneg, ContinuousMultilinearMap.le_opNNNorm, Metric.isCover_zero, nnnorm_cfcₙ_le, ENNReal.coe_lt_one_iff, AffineMap.antilipschitzWith_of_finiteDimensional, Continuous.nnnorm', MeasureTheory.ProbabilityMeasure.coeFn_mk, MeasureTheory.Measure.singularPart_smul_right, MeasureTheory.distribHaarChar_pos, Real.ofNat_le_toNNReal, ContinuousWithinAt.cfc_nnreal, NNReal.image_coe_Icc, ENNReal.coe_natCast, antilipschitzWith_lineMap, ProbabilityTheory.HasSubgaussianMGF_add_of_HasCondSubgaussianMGF, ENNReal.smulCommClass_right, nnnorm_cfcₙ_nnreal_le, BoxIntegral.IntegrationParams.MemBaseSet.exists_common_compl, ENNReal.coe_smul, dimH_def, LinearMap.injective_iff_antilipschitz, NNReal.le_iInf_mul, ENNReal.instPosSMulStrictMonoNNReal, Real.nndist_eq', nnnorm_mul_le_of_le, apply_le_nnnorm_cfcₙ_nnreal, PadicComplex.nnnorm_extends, ENNReal.tendsto_coe_nhds_top, NNReal.HolderTriple.inv_lt_inv, MeasureTheory.FiniteMeasure.map_apply_of_aemeasurable, NNReal.tsum_pos, NNReal.iSup_mul, ContinuousMapZero.continuous_toNNReal, Valuation.RankLeOne.strictMono', MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN, nndist_vadd_vadd_le, Complex.nnnorm_eq_one_of_pow_eq_one, nnnorm_zpow, nnnorm_add_le, NNReal.coe_le_coe, continuousOn_cfcₙ_nnreal_setProd, NumberField.HeightOneSpectrum.one_lt_absNorm_nnreal, NNReal.holderConjugate_iff, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, MeasureTheory.ProbabilityMeasure.toFiniteMeasure_apply_eq_apply, ENNReal.toReal_smul, continuous_nndist, ContinuousAlternatingMap.opNNNorm_prod, measurable_coe_nnreal_ennreal, ENNReal.toNNReal_pos_iff, MeasureTheory.ProbabilityMeasure.prod_apply, NNReal.sqrt_mul_self, LipschitzOnWith.div, NNReal.strictConcaveOn_rpow, aemeasurable_coe_nnreal_ennreal_iff, MeasureTheory.Measure.isAddLeftInvariant_eq_smul, one_le_thickenedIndicator_apply, ProbabilityTheory.setBernoulli_apply, WithLp.unitization_nnnorm_def, edist_smul_le, Real.exists_lt_of_strictMono, NNReal.le_rpow_inv_iff_of_pos, nnnorm_le_add_nnnorm_add', EMetric.NonemptyCompacts.lipschitz_sup, ProbabilityTheory.Kernel.integral_withDensity, Metric.IsSeparated.image_antilipschitz, NNReal.Lp_add_le_tsum, NNReal.inv_lt_one_iff, HasOuterApproxClosed.apprSeq_apply_le_one, MonotoneOn.nnnorm_cfcₙ, range_cfc_nnreal_subset, NNReal.iSup_pow, FormalMultilinearSeries.ofScalars_radius_ge_inv_of_tendsto, NNReal.sqrt_inv, NNReal.image_coe_uIoo, ContDiffAt.exists_lipschitzOnWith, ContDiffWithinAt.exists_lipschitzOnWith, ENNReal.ofNNReal_natCast_add, NNReal.tendsto_cofinite_zero_of_summable, lipschitzWith_min, one_le_nnnorm_one, AntilipschitzWith.add_sub_lipschitzWith, MeasureTheory.JordanDecomposition.real_smul_def, ContinuousMap.nnnorm_sum_eq_sup, nndist_self_homothety, ENNReal.coe_iSup, ENNReal.image_coe_uIcc, LipschitzAdd.lipschitz_add, CFC.nnnorm_nnrpow, FormalMultilinearSeries.radius_eq_liminf, ENNReal.coe_div, MeasureTheory.FiniteMeasure.apply_union_le, NNReal.coe_eq_one, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, Metric.IsCover.image_lipschitz, ENNReal.isEmbedding_coe, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, NNReal.dist_gm_am_le, Matrix.linfty_opNNNorm_def, UniformOnFun.lipschitzWith_restrict, NNReal.coe_list_prod, NumberField.FinitePlace.norm_embedding_int, coe_le_enorm, InformationTheory.klDiv_smul_same, LipschitzWith.subtype_val, CStarRing.nnnorm_star_mul_self, IsUltrametricDist.nnnorm_prod_le_of_forall_le, Metric.lipschitz_infNndist_pt, IsUltrametricDist.nnnorm_add_le_max, HasOuterApproxClosed.exAppr, CFC.norm_nnrpow, CStarAlgebra.nnnorm_le_natCast_iff_of_nonneg, NNReal.Lr_le_Lp_mul_Lq_tsum, ENNReal.coe_div', NNReal.agm_lt_agmSequences_snd_of_ne, HolderWith.interpolate, EMetric.exists_pos_forall_lt_edist, NNReal.coe_sub_of_lt, MeasureTheory.Measure.addHaarScalarFactor_smul, NNReal.nndist_zero_eq_val, NNReal.bddAbove_coe, tsum_geometric_nnreal, nnnorm_pos, NormedField.exists_lt_nnnorm, NNReal.measurable_of_tendsto', Real.toNNReal_lt_toNNReal_iff', Prod.nnnorm_mk, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, Similar.exists_pairwise_edist_eq, LocallyLipschitzOn.exists_lipschitzOnWith_of_compact, ContinuousMapZero.toNNReal_apply, HolderWith.nndist_le, LipschitzWith.zero_iff, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul, InformationTheory.toReal_klDiv_smul_left, CompactlySupportedContinuousMap.nnrealPart_neg_eq_zero_of_nonneg, NNReal.agmSequences_succ, Measurable.nnreal_tsum, LipschitzWith.div, nnnorm_zsmul_le, nndist_homothety_self, NNReal.young_inequality_real, LipschitzOnWith.mul, Tactic.NormNum.isNat_nnrealSqrt, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Mathlib.Meta.NormNum.nnreal_rpow_isRat_eq_inv_nnreal_rpow, ProbabilityTheory.HasSubgaussianMGF_sum_of_HasCondSubgaussianMGF, BoundedContinuousFunction.apply_le_nndist_zero, antilipschitzWith_iff_exists_mul_le_norm, Metric.externalCoveringNumber_zero, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, SpectrumRestricts.nnreal_iff_nnnorm, MeasureTheory.FiniteMeasure.continuous_lintegral_boundedContinuousFunction, Valued.integer.exists_norm_coe_lt_one, ConvexBody.coe_smul', DilationEquiv.ratio_pow, ContinuousAt.nnnorm', BoundedContinuousFunction.nndist_le_two_nnnorm, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, BoundedContinuousFunction.NNReal.upper_bound, MeasureTheory.llr_smul_nnreal_right, CStarAlgebra.le_nnnorm_of_mem_quasispectrum, unitInterval.toNNReal_add_toNNReal_symm, MeasureTheory.Measure.singularPart_smul, NNReal.map_coe_nhdsGE, NNReal.sqrt_lt_sqrt, HolderWith.comp, PiLp.nndist_eq_of_L2, MeasureTheory.Measure.coe_nnreal_smul, CFC.nnrpow_map_prod, IsUltrametricDist.nnnorm_zsmul_le, NNReal.inner_le_Lp_mul_Lq, NNReal.coe_single, ENNReal.toNNReal_inv, measurable_coe_nnreal_real_iff, ENNReal.coe_sInf, MeasureTheory.FiniteMeasure.tendsto_iff_forall_testAgainstNN_tendsto, PadicComplexInt.integers, NNReal.rpow_inv_lt_iff_of_neg, NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le, Polynomial.card_mahlerMeasure_le_prod, Real.natCast_le_toNNReal, MeasureTheory.Measure.euclideanHausdorffMeasure_def, measurable_coe_nnreal_ennreal_iff, Matrix.linfty_opNorm_def, egauge_le_of_smul_mem_of_ne, NumberField.house_eq_sup', CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, ENNReal.coe_indicator, RCLike.lipschitzWith_im, Seminorm.smul_le_smul, MeasureTheory.Measure.addHaarScalarFactor_self, AntilipschitzWith.add_lipschitzWith, MeasureTheory.addEquivAddHaarChar_smul_integral_map, NNReal.instIsScalarTowerOfReal, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, SpectrumRestricts.nnreal_add, NNReal.rpow_sub_intCast', NumberField.FinitePlace.norm_def, ProbabilityTheory.cauchyMeasure_zero_scale, MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto, NNReal.le_of_forall_lt_one_mul_le, unitInterval.toNNReal_one, Dilation.ratio_of_subsingleton, Similar.exists_pairwise_nndist_eq, NNReal.iSup_mul_le, NNReal.lintegral_mul_le_Lp_mul_Lq, ApproximatesLinearOn.to_inv, Real.cast_natAbs_eq_nnabs_cast, NNReal.coe_max, NNReal.exists_mem_Ioc_zpow, Metric.boundedSpace_iff_edist, Metric.exists_pos_forall_lt_edist, holderWith_one, Mathlib.Meta.NormNum.IsInt.nnreal_rpow_eq_inv_nnreal_pow, WithLp.nndist_snd_le, NNReal.coe_sub, Measurable.infNndist, MeasureTheory.Lp.nnnorm_zero, Matrix.norm_eq_sup_sup_nnnorm, Polynomial.IsRoot.norm_lt_cauchyBound, nnnorm_le_pi_nnnorm', NNReal.iInf_const_zero, HolderWith.smul_iff, NNReal.bddAbove_range_natCast_iff, NNReal.rpow_pos, ENNReal.nhds_coe_coe, MeasureTheory.SimpleFunc.map_coe_ennreal_restrict, nnnorm_div_le, BoundedContinuousFunction.lintegral_le_edist_mul, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, nndist_lineMap_left, NNReal.sq_sqrt, NNReal.tendsto_pow_atTop_nhds_zero_iff, IsUltrametricDist.nnnorm_tsum_le, PadicComplex.isAlgClosed, MeasureTheory.measureReal_nnreal_smul_apply, UniformOnFun.lipschitzWith_one_ofFun_toFun', MeasureTheory.exists_pos_lintegral_lt_of_sigmaFinite, NNReal.agm_le_max, NNReal.summable_rpow, IsSelfAdjoint.nnnorm_pow_two_pow, nndist_pi_eq_iff, MeasureTheory.FiniteMeasure.mass_pi, PiLp.nndist_eq_iSup, Continuous.cfcₙ_nnreal', thickenedIndicator.coeFn_eq_comp, NNReal.HolderTriple.one_div_pos', CFC.nnrpow_two, ContinuousAlternatingMap.le_of_opNNNorm_le, HolderWith.of_le_of_le, Nonneg.instIsometricContinuousFunctionalCalculus, MeasureTheory.Content.sup_le', HasSum.isProbabilityMeasure_sum_dirac_nnreal, LipschitzWith.nnorm_le_mul, isProperMap_nndist, NNReal.Icc_subset_segment, Real.natCast_lt_toNNReal, NNReal.holderTriple_iff, ENNReal.coe_injective, PiLp.nndist_eq_of_L1, ContinuousLinearMap.antilipschitz_of_forall_le_inner_map, FormalMultilinearSeries.comp_summable_nnreal, LipschitzWith.dist, NNReal.concaveOn_rpow, Valued.integer.norm_irreducible_pos, WithLp.prod_antilipschitzWith_ofLp, rieszContentAux_le, ProbabilityTheory.setBernoulli_eq_map, HolderWith.nndist_le_of_le, NNReal.finset_sup_div, ENNReal.toNNReal_zero, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto, measurable_nnnorm, Delone.DeloneSet.coveringRadius_pos, ProbabilityTheory.Kernel.HasSubgaussianMGF.fun_zero, ENNReal.image_coe_Ioc, thickenedIndicator_mono, MeasureTheory.BorelCantelli.process_difference_le, BoundedContinuousFunction.integrable_of_nnreal, NNReal.instCompleteSpace, NNReal.rpow_left_bijective, lipschitzWith_one_norm, ContinuousMap.nnnorm_sub_eq_max, UniformFun.lipschitzWith_eval, NNReal.coe_sInf, ContinuousMap.exists_mul_le_one_eqOn_ge, IsCoercive.antilipschitz, MeasureTheory.FiniteMeasure.null_iff_toMeasure_null, CFC.nnrpow_add, NNReal.instContinuousStar, nnnorm_cfcₙ_lt, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isOpen
bridge: BoxIntegral.IntegrationParams.MemBaseSet.exists_compl, BoxIntegral.IntegrationParams.MemBaseSet.distortion_le
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