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Theorems · Theorem · measure theory

MeasureTheory.Integrable.congr

∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] {f g : α → ε}, MeasureTheory.Integrable f μ → f =ᵐ[μ] g → MeasureTheory.Integrable g μ
Defined in
Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by
28 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceContinuousENorm

Around this declaration

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

MeasureTheory.integrable_congr · cited by 42MeasureTheory.integrable_…MeasureTheory.integrable_condExp · cited by 28MeasureTheory.integrable_…MeasureTheory.Martingale.integrable · cited by 10Martingale.integrableMeasureTheory.setToFun_congr_ae · cited by 10MeasureTheory.setToFun_co…MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' · cited by 5MeasureTheory.ae_eq_of_fo…MeasureTheory.IntegrableOn.congr_fun_ae · cited by 5IntegrableOn.congr_fun_aeMeasureTheory.IntegrableOn.of_ae_sdiff_eq_zero · cited by 4IntegrableOn.of_ae_sdiff_…MeasureTheory.setIntegral_eq_of_subset_of_ae_sdiff_eq_zero · cited by 4MeasureTheory.setIntegral…MeasureTheory.WithDensityᵥEq.congr_ae · cited by 3WithDensityᵥEq.congr_aeMeasureTheory.SignedMeasure.eq_singularPart · cited by 3SignedMeasure.eq_singular…MeasureTheory.L1.SimpleFunc.setToL1S_nonneg · cited by 3SimpleFunc.setToL1S_nonnegintegrableOn_mul_sum_Icc · cited by 3integrableOn_mul_sum_IccMeasureTheory.IntegrableAtFilter.congr · cited by 2IntegrableAtFilter.congrMeasureTheory.Integrable.of_subsingleton_codomain · cited by 1Integrable.of_subsingleto…ValueDistribution.Cartan.integrable_integral_norm_cartanKernel · cited by 1Cartan.integrable_integra…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableContinuousENorm · cited by 290ContinuousENormMeasureTheory.AEStronglyMeasurable.congr · cited by 19AEStronglyMeasurable.congrMeasureTheory.HasFiniteIntegral.congr · cited by 3HasFiniteIntegral.congrIntegrable.congrCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.