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Theorems · Theorem · measure theory

AEMeasurable.restrict

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {f : α → β}
  {μ : MeasureTheory.Measure α}, AEMeasurable f μ → ∀ {s : Set α}, AEMeasurable f (μ.restrict s)
Defined in
Mathlib.MeasureTheory.Measure.AEMeasurable
Cited by
23 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace

Around this declaration

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

MeasureTheory.lintegral_eq_zero_iff' · cited by 16MeasureTheory.lintegral_e…MeasureTheory.withDensity_absolutelyContinuous' · cited by 5MeasureTheory.withDensity…MeasureTheory.withDensity_mul₀ · cited by 5MeasureTheory.withDensity…MeasureTheory.measure_le_laverage_pos · cited by 3MeasureTheory.measure_le_…MeasureTheory.withDensity_apply_eq_zero' · cited by 2MeasureTheory.withDensity…MeasureTheory.ae_le_of_forall_setLIntegral_le_of_sigmaFinite₀ · cited by 2MeasureTheory.ae_le_of_fo…MeasureTheory.setLIntegral_tilted' · cited by 2MeasureTheory.setLIntegra…MeasureTheory.setLIntegral_trim_ae · cited by 2MeasureTheory.setLIntegra…MeasureTheory.setIntegral_tilted' · cited by 2MeasureTheory.setIntegral…MeasureTheory.AEMeasurable.ae_eq_of_forall_setLIntegral_eq · cited by 2AEMeasurable.ae_eq_of_for…AEMeasurable.indicator · cited by 2AEMeasurable.indicatorMeasureTheory.toReal_condLExp · cited by 2MeasureTheory.toReal_cond…ProbabilityTheory.setLIntegral_toKernel_prod · cited by 1ProbabilityTheory.setLInt…MeasureTheory.condLExp_add_left · cited by 1MeasureTheory.condLExp_ad…MeasureTheory.setIntegral_tilted · cited by 1MeasureTheory.setIntegral…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.restrict · cited by 1646Measure.restrictAEMeasurable · cited by 840AEMeasurableAEMeasurable.mk · cited by 75AEMeasurable.mkAEMeasurable.ae_eq_mk · cited by 65AEMeasurable.ae_eq_mkAEMeasurable.measurable_mk · cited by 62AEMeasurable.measurable_mkMeasureTheory.ae_restrict_of_ae · cited by 46MeasureTheory.ae_restrict…AEMeasurable.restrictCITED BYCITES

Cites9

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Cited by23

Results whose statement or proof uses this declaration.