Documentation Verification Report

Lp

šŸ“ Source: Mathlib/MeasureTheory/Function/StronglyMeasurable/Lp.lean

Statistics

MetricCount
DefinitionsLp
1
TheoremsaefinStronglyMeasurable, finStronglyMeasurable, aefinStronglyMeasurable, finStronglyMeasurable_of_stronglyMeasurable
4
Total5

MeasureTheory

Definitions

NameCategoryTheorems
Lp šŸ“–CompOp
607 mathmath: SchwartzMap.norm_toLp_le_seminorm, L1.setToL1_eq_setToL1', Lp.instHasSolidNorm, integrable_indicatorConstLp, ContinuousMap.toLp_inj, Lp.toTemperedDistributionCLM_apply, LpToLpRestrictCLM_coeFn, L1.SimpleFunc.norm_Integral_le_one, Lp.tendsto_Lp_iff_tendsto_eLpNorm'', condExpInd_of_measurable, Lp.mul_meas_ge_le_pow_enorm', condExpL1_smul, Lp.instIsScalarTower, DomAddAct.mk_vadd_indicatorConstLp, aestronglyMeasurable_condExpInd, mem_lpMeasSubgroup_iff_aestronglyMeasurable, ContinuousLinearMap.integral_compLp, Lp.compMeasurePreserving_id_apply, norm_indicatorConstLp_le, condExpInd_ae_eq_condExpIndSMul, L1.setToL1_indicatorConstLp, L1.SimpleFunc.setToL1SCLM_add_left, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, UnitAddTorus.coe_mFourierBasis, SchwartzMap.inner_fourier_toL2_eq, SchwartzMap.toLp_fourierTransformInv_eq, L2.inner_indicatorConstLp_eq_inner_setIntegral, Lp.mem_Lp_of_ae_bound, tendsto_condExpL1_of_dominated_convergence, Lp.const_smul_mem_Lp, norm_condExpL2_le, Lp.instIsOrderedAddMonoid, MemLp.toLp_val, Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm, ContinuousLinearMap.continuous_integral_comp_L1, Lp.edist_def, L1.norm_setToL1_le, inner_condExpL2_left_eq_right, ContinuousMap.toLp_denseRange, Lp.coeFn_add, ContinuousLinearMap.comp_memLp, Lp.eq_zero_iff_ae_eq_zero, Lp.ext_iff, ContinuousLinearMap.norm_compLp_le, condExpL2_ae_eq_zero_of_ae_eq_zero, Lp.indicatorConstLp_compMeasurePreserving, Lp.coeFn_const, norm_setToFun_le_mul_norm', LipschitzWith.lipschitzWith_compLp, norm_indicatorConstLp, ContinuousMap.range_toLp, L1.ofReal_norm_eq_lintegral, condExpIndL1Fin_smul, Lp.dist_def, Lp.aestronglyMeasurable, L1.SimpleFunc.setToL1SCLM_const, lpMeasSubgroupToLpTrim_neg, Lp.nnnorm_le_of_ae_bound, Lp.simpleFunc.uniformContinuous, Lp.memLp, Lp.nnnorm_def, Integrable.toL1_zero, Lp.mem_Lp_of_ae_le, lpMeasSubgroupToLpTrim_ae_eq, condExpIndL1_add, L1.norm_setToL1_le_norm_setToL1SCLM, norm_indicatorConstLp_top, L1.integral_smul, Lp.instFourierInvSMul, ContinuousLinearMap.smul_compLp, AEEqFun.compMeasurePreserving_mem_Lp, L2.inner_def, Lp.enorm_toLp, SchwartzMap.toLpCLM_apply, condExpIndL1Fin_add, Lp.compMeasurePreservingā‚—_apply, ContinuousMap.toLp_norm_le, condExpL1_measure_zero, SchwartzMap.inner_toL2_toL2_eq, AEEqFun.integrable_iff_mem_L1, Lp.simpleFunc.isDenseEmbedding, Integrable.toL1_coeFn, Lp.ae_eq_zero_of_forall_setIntegral_eq_zero', L1.SimpleFunc.norm_setToL1S_le, MemLp.condExpL2_ae_eq_condExp, DomMulAct.smul_Lp_sub, SchwartzMap.norm_toLp_one, L1.SimpleFunc.setToL1S_neg, SchwartzMap.toLp_fourierInv_eq, continuous_condExpIndL1, Lp.nnnorm_eq_zero_iff, dominatedFinMeasAdditive_condExpInd, L1.SimpleFunc.integral_add, Integrable.edist_toL1_zero, Lp.finStronglyMeasurable, aestronglyMeasurable_condExpL2, L1.setToL1_smul_left, L1.setToL1_zero_left, ContinuousAt.compMeasurePreservingLp, condExpInd_nonneg, condExpL1_of_aestronglyMeasurable', L1.continuous_integral, Lp.stronglyMeasurable, L1.integrable_coeFn, SchwartzMap.injective_toLp, condExpL2_indicator_ae_eq_smul, condExpL1CLM_of_aestronglyMeasurable', UnitAddTorus.mFourierCoeff_toLp, Lp.dist_edist, ContinuousLinearMap.holderā‚—_apply_apply, Lp.edist_eq_eLpNorm_neg_add, L1.SimpleFunc.setToL1SCLM_zero_left', Lp.coeFn_mk, Lp.norm_zero, Lp.mem_Lp_of_ae_nnnorm_bound, continuous_setToFun, Lp.simpleFunc.sub_toSimpleFunc, L1.dist_eq_integral_dist, L1.norm_def, integral_condExpL2_eq, DomAddAct.instIsIsometricVAddSubtypeAEEqFunMemAddAddSubgroupLp, Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul, Lp.edist_toLp_toLp, orthonormal_fourier, Lp.simpleFunc.smul_toSimpleFunc, setIntegral_condExpL2_indicator, L1.SimpleFunc.integral_eq_norm_posPart_sub, Integrable.norm_toL1, ContinuousLinearMap.setIntegral_compLp, Lp.edist_toLp_zero, L1.setToL1_mono_left', DomAddAct.vadd_Lp_add, Integrable.toL1_eq_mk, condExpIndSMul_empty, lintegral_nnnorm_condExpL2_indicator_le, setIntegral_condExpInd, edist_indicatorConstLp_eq_enorm, Lp.compMeasurePreserving_comp, Lp.ae_eq_zero_of_forall_setIntegral_eq_zero, L1.setToL1_eq_setToL1SCLM, norm_condExpL2_coe_le, setLIntegral_nnnorm_condExpL2_indicator_le, mem_lpMeas_iff_aestronglyMeasurable, L1.setToL1_nonneg, aestronglyMeasurable_condExpL1, SchwartzMap.norm_fourier_toL2_eq, Lp.boundedContinuousFunction_topologicalClosure, Lp.SecondCountableTopology, Lp.instCompleteSpace, Lp.norm_toLp, Lp.instFourierPair, L1.integral_def, BoundedContinuousFunction.Lp_nnnorm_le, DomMulAct.edist_smul_Lp, hasSum_fourier_series_L2, L1.SimpleFunc.setToL1S_smul_real, BoundedContinuousFunction.range_toLpHom, BoundedContinuousFunction.toLp_inj, mem_lpMeas_indicatorConstLp, BoundedContinuousFunction.toLp_injective, integral_indicatorConstLp, Lp.coeFn_compMeasurePreserving, condExpIndSMul_smul, lintegral_nnnorm_condExpL2_le, StrongDual.toLp_of_not_memLp, Lp.compMeasurePreservingā‚—įµ¢_apply_coe, Lp.dist_eq_eLpNorm_neg_add, L1.setToFun_eq_setToL1, SchwartzMap.norm_fourierTransformCLM_toL2_eq, enorm_indicatorConstLp_le, Lp.norm_neg, L1.integral_eq_setToL1, Integrable.toL1_smul, Lp.nnnorm_neg, ContinuousLinearMap.holder_smul_left, Lp.coeFn_smul, DomMulAct.mk_smul_toLp, condExpL1CLM_indicatorConstLp, L1.setToL1_add_left', L1.SimpleFunc.coe_negPart, integrableOn_Lp_of_measure_ne_top, L1.setToL1_mono_left, Lp.dist_eq_norm, condExpInd_disjoint_union, Lp.coeFn_le, Lp.simpleFunc.add_toSimpleFunc, UnitAddTorus.coeFn_mFourierLp, setIntegral_condExpIndSMul, indicatorConstLp_univ, lpMeasToLpTrimLie_symm_indicator, norm_setToFun_le', Lp.norm_const_le, Lp.coeFn_negPart_eq_max, Lp.ae_eq_of_forall_setIntegral_eq', condExpL1_undef, Lp.nnnorm_toLp, Measure.MeasureDense.indicatorConstLp_subset_closure, L1.SimpleFunc.setToL1S_sub, ContinuousMap.toLp_def, L2.integral_inner_eq_sq_eLpNorm, ContinuousWithinAt.compMeasurePreservingLp, Lp.norm_le_norm_of_ae_le, L2.inner_indicatorConstLp_one, L2.inner_indicatorConstLp_indicatorConstLp, L1.setToL1_smul_left', Lp.boundedContinuousFunction_dense, Lp.constā‚—_apply, Lp.coe_nnnorm, L1.SimpleFunc.toLp_one_eq_toL1, Lp.mem_boundedContinuousFunction_iff, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, condExpIndSMul_add, Lp.norm_fourier_eq, SchwartzMap.coeFn_toLp, Lp.instFourierSMul, L1.SimpleFunc.setToL1SCLM_congr_left, Lp.simpleFunc.toLp_eq_toLp, Lp.norm_const', norm_condExpIndL1_le, SchwartzMap.norm_toLp, condExpL1_add, Real.Lp.fourierTransform_apply, Lp.smul_zero, L1.SimpleFunc.norm_eq_sum_mul, DomMulAct.mk_smul_indicatorConstLp, norm_condExpInd_apply_le, ContinuousLinearMap.nnnorm_holder_apply_apply_le, DomAddAct.norm_vadd_Lp, condExpL1_neg, Lp.instTrivialStarSubtypeAEEqFunMemAddSubgroup, L1.nnnorm_integral_le, Lp.norm_smul_le, isClosed_aestronglyMeasurable, Lp.coeFn_sup, Lp_toLp_restrict_add, setIntegral_condExpL1, condExpIndL1_smul, UnitAddTorus.orthonormal_mFourier, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Integrable.enorm_toL1, continuous_integral_integral, fourierCoeff_toLp, coe_fourierBasis, lpMeasSubgroupToLpTrim_sub, Integrable.toL1_sub, MemLp.toLp_neg, ProbabilityTheory.Kernel.continuous_integral_integral, DomMulAct.smul_Lp_neg, L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, integral_condExpL2_eq_of_fin_meas_real, Lp.simpleFunc.denseRange, memL1_smul_of_L1_withDensity, condExp_ae_eq_condExpL1, condExpIndL1_smul', BoundedContinuousFunction.mem_Lp, lpMeasSubgroupToLpTrim_right_inv, Filter.Tendsto.compMeasurePreservingLp, BoundedContinuousFunction.Lp_norm_le, DomAddAct.vadd_Lp_ae_eq, Lp.norm_constL_le, Lp.simpleFunc.neg_toSimpleFunc, DomMulAct.norm_smul_Lp, condExpL2_indicator_of_measurable, Lp.add_smul, setIntegral_condExpL1CLM_of_measure_ne_top, condExp_ae_eq_condExpL1CLM, DomAddAct.vadd_Lp_sub, BoundedContinuousFunction.coeFn_toLp, Integrable.toL1_smul', UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, Lp.instContinuousVAddDomAddAct, condExpL2_indicator_eq_toSpanSingleton_comp, L1.tendsto_setToL1, L1.SimpleFunc.norm_setToL1SCLM_le', condExpL1CLM_indicatorConst, mem_lpMeasSubgroup_toLp_of_trim, L1.nnnorm_Integral_le_one, lpMeasSubgroupToLpTrim_add, L1.integral_eq_norm_posPart_sub, Lp.instContinuousFourierInv, UnitAddTorus.hasSum_mFourier_series_L2, Lp.norm_const, instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, lpMeasSubgroupToLpTrim_left_inv, lintegral_nnnorm_condExpL2_indicator_le_real, L1.setToL1_unique, Lp.instAddLeftMono, L1.SimpleFunc.setToL1SCLM_smul_left, ContinuousLinearMap.lpPairing_eq_integral, Lp.simpleFunc.norm_toSimpleFunc, ContinuousLinearMap.holder_smul_right, L2.eLpNorm_inner_lt_top, L1.SimpleFunc.setToL1SCLM_smul_left', condExpL1CLM_lpMeas, Lp.mem_Lp_iff_memLp, SchwartzMap.norm_fourier_Lp_top_leq_toLp_one, StrongDual.toLpā‚—_apply, L1.setToL1_apply_coeToLp, Lp.const_mem_Lp, Lp.compMeasurePreserving_comp_apply, indicatorConstLp_add, L1.setToL1_congr_left', DomAddAct.vadd_Lp_neg, Lp.simpleFunc.coeFn_le, Lp.instFourierPairInv, Lp.norm_le_of_ae_bound, SchwartzMap.norm_toLp', Lp.simpleFunc.toLp_zero, L2.inner_indicatorConstLp_eq_setIntegral_inner, L1.SimpleFunc.integralCLM'_L1_eq_integral, Lp.coeFn_nonneg, Lp.toLp_coeFn, nnnorm_indicatorConstLp_le, DomMulAct.dist_smul_Lp, Lp.instFourierInvAdd, L1.setToL1_congr_left, L1.setToL1_smul, Lp.coeFn_lpSMul, Lp.simpleFunc.coeFn_zero, condExpIndSMul_nonneg, L1.dist_def, ContinuousLinearMap.coeFn_compLpL, Real.Lp.fourierTransformCLM_apply, StrongDual.norm_toLpā‚—_le, Lp.coe_mk, Lp.instIsCentralScalar, L1.SimpleFunc.setToL1SCLM_congr_left', L1.norm_integral_le, setIntegral_indicatorConstLp, ProbabilityTheory.Kernel.continuous_integral_integral_comp, ContinuousMap.toLp_injective, StrongDual.toLpā‚—_of_not_memLp, indicatorConstLp_sub, DomAddAct.edist_vadd_Lp, L1.aemeasurable_coeFn, integrable_condExpL2_of_isFiniteMeasure, condExpIndL1Fin_disjoint_union, Lp.tendsto_Lp_of_tendsto_eLpNorm, Lp.instIsBoundedSMul, ContinuousMap.coe_toLp, DomMulAct.instIsIsometricSMulSubtypeAEEqFunMemAddSubgroupLp, Lp.antitone, SchwartzMap.norm_toLp_top_le, ContinuousLinearMap.integral_comp_L1_comm, span_fourierLp_closure_eq_top, L1.measurable_coeFn, aestronglyMeasurable_condExpL1CLM, SchwartzMap.inner_fourierTransformCLM_toL2_eq, continuous_integral, Lp.simpleFunc.isBoundedSMul, Lp.coe_posPart, integrable_condExpL2_indicator, Lp.zero_smul, DomMulAct.smul_Lp_zero, DomAddAct.mk_vadd_toLp, lpMeasSubgroupToLpTrim_norm_map, MemLp.condExpL2_ae_eq_condExp', Lp.completeSpace_lp_of_cauchy_complete_eLpNorm, Lp.simpleFunc.toLp_sub, Lp.simpleFunc.coe_smul, Lp.smul_def, Lp.norm_exponent_zero, Lp.smul_neg, L1.stronglyMeasurable_coeFn, ContinuousMap.coeFn_toLp, L1.norm_setToL1_le_mul_norm', Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq, tendstoInMeasure_of_tendsto_Lp, ProbabilityTheory.condVar_of_sigmaFinite, Lp.instSMulCommClass, Lp.simpleFunc.toLp_neg, L1.SimpleFunc.integral_smul, L2.inner_indicatorConstLp_one_indicatorConstLp_one, lpTrimToLpMeas_ae_eq, DomAddAct.vadd_Lp_const, L1.SimpleFunc.norm_setToL1SCLM_le, ContinuousMap.toLp_comp_toContinuousMap, L1.SimpleFunc.setToL1SCLM_congr_measure, Lp.smul_comm, SchwartzMap.continuous_toLp, isComplete_aestronglyMeasurable, Lp.simpleFunc.isUniformEmbedding, L1.integral_of_fun_eq_integral, L1.integral_zero, SchwartzMap.toLp_fourierTransform_eq, setLIntegral_nnnorm_condExpIndSMul_le, continuous_indicatorConstLp_set, condExpIndL1_of_not_measurableSet, Lp.smul_add, L1.norm_setToL1_le', withDensitySMulLI_apply, Lp.fourierInv_toTemperedDistribution_eq, UnitAddTorus.hasSum_prod_mFourierCoeff, DomMulAct.smul_Lp_ae_eq, Lp.simpleFunc.isUniformInducing, L1.norm_of_fun_eq_integral_norm, L1.integral_add, Lp.mem_Lp_iff_eLpNorm_lt_top, aestronglyMeasurable_condExpIndSMul, Lp.constL_apply, L2.mem_L1_inner, L1.integral_eq_integral, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp, Integrable.coeFn_toL1, Lp.simpleFunc.coe_indicatorConst, condExpIndL1_disjoint_union, ContinuousLinearMap.add_compLp, Lp.inner_fourier_eq, Integrable.norm_toL1_eq_lintegral_norm, L1.aestronglyMeasurable_coeFn, condExpInd_smul', L1.setToL1_add_left, Lp.eLpNorm_lt_top, L2.integrable_inner, SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_one, BoundedContinuousFunction.toLp_norm_le, Lp.continuous_negPart, Lp.coeFn_negPart, condExp_of_sigmaFinite, norm_setToFun_le_mul_norm, L1.SimpleFunc.norm_eq_integral, condExpIndL1_of_measure_eq_top, L1.SimpleFunc.norm_integral_le_norm, Lp.simpleFunc.toLp_smul, L1.norm_setToL1_le_mul_norm, MemLp.coeFn_toLp, L1.SimpleFunc.setToL1SCLM_mono_left', Lp.neg_smul, Lp.instOrderClosedTopologySubtypeAEEqFunMemAddSubgroupOfClosedIciTopology, Lp.mem_Lp_of_nnnorm_ae_le_mul, norm_condExpInd_le, setToFun_mono_left, MemLp.toLp_add, inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, Lp.coeFn_zero, mem_lpMeas_self, norm_Lp_toLp_restrict_le, Lp.coe_LpSubmodule, integrableOn_condExpL2_of_measure_ne_top, hasSum_sq_fourierCoeff, ContinuousLinearMap.holder_add_right, Lp.enorm_def, condExpInd_disjoint_union_apply, ContinuousLinearMap.add_compLpL, L1.setToL1_simpleFunc_indicatorConst, Lp.tendsto_Lp_iff_tendsto_eLpNorm', L1.SimpleFunc.setToL1SCLM_zero_left, UnitAddTorus.mFourierBasis_repr, condExpIndL1Fin_ae_eq_condExpIndSMul, Lp.norm_measure_zero, tendsto_indicatorConstLp_set, LipschitzWith.coeFn_compLp, Lp.ker_toTemperedDistributionCLM_eq_bot, fourierBasis_repr, L1.setToL1_zero_left', BoundedContinuousFunction.inner_toLp, condExpL1_mono, Lp.coeFn_neg, L1.norm_Integral_le_one, Lp.toLp_compMeasurePreserving, Lp.coeFn_abs, Lp.norm_eq_zero_iff, Lp.coeFn_sub, Lp.mem_Lp_of_nnnorm_ae_le, Lp.meas_ge_le_mul_pow_enorm, UnitAddTorus.hasSum_sq_mFourierCoeff, ContinuousLinearMap.coeFn_compLp, DomMulAct.nnnorm_smul_Lp, L1.setToL1_mono, lintegral_nnnorm_condExpIndSMul_le, LipschitzWith.continuous_compLp, Lp.smul_assoc, integrable_condExpIndSMul, Lp.toTemperedDistribution_apply, LipschitzWith.compLp_zero, condExpL1_zero, Lp.compMeasurePreserving_continuous, Lp.coeFn_posPart, L1.SimpleFunc.setToL1S_add, Lp.mem_Lp_of_ae_le_mul, L1.norm_sub_eq_lintegral, norm_indicatorConstLp', Lp.neg_smul_neg, isometry_lpMeasSubgroupToLpTrim, integrable_condExpL1, ContinuousLinearMap.smul_compLpL, Integrable.toL1_add, ContinuousLinearMap.norm_compLpL_le, DomMulAct.smul_Lp_const, L1.SimpleFunc.setToL1SCLM_mono_left, Lp.ae_eq_of_forall_setIntegral_eq, setIntegral_condExpL1CLM, L1.hasFiniteIntegral_coeFn, tsum_sq_fourierCoeff, lpMeasToLpTrim_ae_eq, eLpNorm_condExpL2_le, L1.integral_eq', lpMeasToLpTrim_smul, Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg, L1.SimpleFunc.setToL1SCLM_mono, Lp.compMeasurePreserving_id, condExpIndSMul_ae_eq_smul, Lp.simpleFunc.isDenseInducing, Lp.dense_hasCompactSupport_contDiff, ContinuousLinearMap.norm_holderL_le, lpMeas.ae_fin_strongly_measurable', L1.setToL1'_eq_setToL1SCLM, condExpL1_sub, instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace, Real.Lp.coe_fourierTransform, lpTrimToLpMeasSubgroup_ae_eq, L1.SimpleFunc.setToL1SCLM_nonneg, L1.integral_sub, L1.ofReal_norm_sub_eq_lintegral, Lp.coeFn_inf, ContinuousMap.inner_toLp, L1.SimpleFunc.integral_L1_eq_integral, Lp.simpleFunc.toLp_eq_mk, DomAddAct.dist_vadd_Lp, ContinuousLinearMap.holderL_apply_apply, Lp.instContinuousFourier, DomAddAct.vadd_Lp_zero, condExpInd_empty, SchwartzMap.norm_fourier_apply_le_toLp_one, condExpL1CLM_smul, LipschitzWith.norm_compLp_le, L1.edist_def, Lp.simpleFunc.toSimpleFunc_eq_toFun, continuous_setIntegral, MemLp.toLp_zero, UnitAddTorus.span_mFourierLp_closure_eq_top, Lp.pow_mul_meas_ge_le_enorm, lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero, condExpIndL1Fin_smul', ContinuousLinearMap.norm_holder_apply_apply_le, Lp.edist_dist, BoundedContinuousFunction.range_toLp, indicatorConstLp_disjoint_union, L1.integral_eq, indicatorConstLp_coeFn, Continuous.compMeasurePreservingLp, Lp.fourier_toTemperedDistribution_eq, Lp.const_val, Lp.simpleFunc.coeFn_nonneg, SimpleFunc.tendsto_approxOn_range_Lp, L1.setToL1'_apply_coeToLp, SchwartzMap.denseRange_toLpCLM, ContinuousOn.compMeasurePreservingLp, memLp_trim_of_mem_lpMeasSubgroup, SchwartzMap.toLp_fourier_eq, DomMulAct.smul_Lp_val, DomAddAct.nnnorm_vadd_Lp, L1.setToL1_const, norm_condExpIndL1Fin_le, lpMeasToLpTrimLie_symm_toLp, continuous_L1_toL1, Lp.tendsto_Lp_iff_tendsto_eLpNorm, indicatorConstLp_empty, Integrable.edist_toL1_toL1, MemLp.toLp_const_smul, Lp.norm_le_mul_norm_of_ae_le_mul, L1.setToL1_lipschitz, Integrable.toL1_neg, norm_condExpL2_le_one, setToFun_eq, condExpL2_comp_continuousLinearMap, Lp.coeFn_star, L2.eLpNorm_rpow_two_norm_lt_top, ContinuousLinearMap.holder_add_left, dist_indicatorConstLp_eq_norm, LipschitzWith.norm_compLp_sub_le, Lp.simpleFunc.toLp_add, BoundedContinuousFunction.toLp_denseRange, condExpL2_const_inner, Lp.isometry_compMeasurePreserving, coeFn_fourierLp, Lp.simpleFunc.dense, Lp.instFourierAdd, Lp.simpleFunc.zero_toSimpleFunc, norm_setToFun_le, Lp.toTemperedDistribution_smul_eq, Lp_toLp_restrict_smul, condExpL1_eq, DomAddAct.vadd_Lp_val, L1.SimpleFunc.coe_posPart, Lp.compMeasurePreserving_val, ContinuousLinearMap.coeFn_holder, Lp.instContinuousSMulDomMulAct, Lp.norm_compMeasurePreserving, Lp.nnnorm_zero, setToFun_toL1, condExpL2_indicator_nonneg, L1.integral_neg, MemLp.toLp_sub, L1.SimpleFunc.setToL1SCLM_add_left', Lp.mul_meas_ge_le_pow_enorm, Lp.simpleFunc.norm_toLp, DomMulAct.smul_Lp_add, Lp.continuous_posPart, Lp.norm_def, ContinuousLinearMap.coeFn_compLp', MemLp.toLp_const, lpMeas.aestronglyMeasurable, L1.SimpleFunc.setToL1S_smul, Lp.compMeasurePreserving_iterate, L1.norm_eq_integral_norm

MeasureTheory.Integrable

Theorems

NameKindAssumesProvesValidatesDepends On
aefinStronglyMeasurable šŸ“–mathematicalMeasureTheory.Integrable
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
SeminormedAddGroup.toContinuousENorm
SeminormedAddCommGroup.toSeminormedAddGroup
MeasureTheory.AEFinStronglyMeasurable
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NormedAddCommGroup.toAddCommGroup
—MeasureTheory.MemLp.aefinStronglyMeasurable
MeasureTheory.memLp_one_iff_integrable
one_ne_zero
NeZero.charZero_one
ENNReal.instCharZero
ENNReal.coe_ne_top

MeasureTheory.Lp

Theorems

NameKindAssumesProvesValidatesDepends On
finStronglyMeasurable šŸ“–mathematical—MeasureTheory.FinStronglyMeasurable
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NormedAddCommGroup.toAddCommGroup
MeasureTheory.AEEqFun.cast
MeasureTheory.AEEqFun
AddSubgroup
MeasureTheory.AEEqFun.instAddGroup
NormedAddGroup.toAddGroup
NormedAddCommGroup.toNormedAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
MeasureTheory.Lp
—SeminormedAddCommGroup.toIsTopologicalAddGroup
MeasureTheory.MemLp.finStronglyMeasurable_of_stronglyMeasurable
memLp
stronglyMeasurable

MeasureTheory.MemLp

Theorems

NameKindAssumesProvesValidatesDepends On
aefinStronglyMeasurable šŸ“–mathematicalMeasureTheory.MemLp
ContinuousENorm.toENorm
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddCommGroup.toSeminormedAddCommGroup
SeminormedAddGroup.toContinuousENorm
SeminormedAddCommGroup.toPseudoMetricSpace
MeasureTheory.AEFinStronglyMeasurable
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NormedAddCommGroup.toAddCommGroup
—MeasureTheory.Measure.instOuterMeasureClass
aestronglyMeasurable
finStronglyMeasurable_of_stronglyMeasurable
MeasureTheory.memLp_congr_ae
finStronglyMeasurable_of_stronglyMeasurable šŸ“–mathematicalMeasureTheory.MemLp
ContinuousENorm.toENorm
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddCommGroup.toSeminormedAddCommGroup
SeminormedAddGroup.toContinuousENorm
SeminormedAddCommGroup.toPseudoMetricSpace
MeasureTheory.StronglyMeasurable
MeasureTheory.FinStronglyMeasurable
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NormedAddCommGroup.toAddCommGroup
—BorelSpace.opensMeasurable
MeasureTheory.StronglyMeasurable.measurable
PseudoEMetricSpace.pseudoMetrizableSpace
Set.union_singleton
MeasureTheory.StronglyMeasurable.separableSpace_range_union_singleton
MeasureTheory.SimpleFunc.memLp_approxOn_range
MeasureTheory.SimpleFunc.measure_support_lt_top_of_memLp
MeasureTheory.SimpleFunc.tendsto_approxOn
subset_closure

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