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Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_congr_ae

∀ {α : Type u_1} {ε : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} [inst : ENorm ε]
  {f g : α → ε}, f =ᵐ[μ] g → MeasureTheory.eLpNorm f p μ = MeasureTheory.eLpNorm g p μ
Defined in
Mathlib.MeasureTheory.Function.LpSeminorm.Basic
Cited by
48 results in Mathlib
Foundations
Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ENorm

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Lp.norm_toLp · cited by 7Lp.norm_toLpMeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm' · cited by 5Lp.tendsto_Lp_iff_tendsto…MeasureTheory.MemLp.eLpNorm_indicator_le · cited by 5MemLp.eLpNorm_indicator_leMeasureTheory.eLpNorm_aeeqFun · cited by 4MeasureTheory.eLpNorm_aee…MeasureTheory.norm_indicatorConstLp · cited by 4MeasureTheory.norm_indica…MeasureTheory.UnifIntegrable.ae_eq · cited by 4UnifIntegrable.ae_eqMeasureTheory.memLp_congr_ae · cited by 4MeasureTheory.memLp_congr…MeasureTheory.Lp.edist_toLp_toLp · cited by 4Lp.edist_toLp_toLpMeasureTheory.UniformIntegrable.ae_eq · cited by 4UniformIntegrable.ae_eqSchwartzMap.denseRange_toLpCLM · cited by 3SchwartzMap.denseRange_to…SchwartzMap.norm_toLp · cited by 3SchwartzMap.norm_toLpMeasureTheory.uniformIntegrable_of · cited by 3MeasureTheory.uniformInte…MeasureTheory.Lp.nnnorm_zero · cited by 2Lp.nnnorm_zeroMeasureTheory.AEEqFun.eLpNorm_compMeasurePreserving · cited by 2AEEqFun.eLpNorm_compMeasu…MeasureTheory.Lp.dist_eq_eLpNorm_neg_add · cited by 2Lp.dist_eq_eLpNorm_neg_addMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqFilter.Eventually.mono · cited by 646Eventually.monoMeasureTheory.eLpNorm · cited by 329MeasureTheory.eLpNormENorm · cited by 155ENormMeasureTheory.eLpNorm_congr_enorm_ae · cited by 3MeasureTheory.eLpNorm_con…MeasureTheory.eLpNorm_congr_aeCITED BYCITES

Cites9

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Cited by48

Results whose statement or proof uses this declaration.