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)- 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- AEMeasurablestatement and proof · cited by 840
- AEMeasurable.mkproof · cited by 75
- AEMeasurable.ae_eq_mkproof · cited by 65
- AEMeasurable.measurable_mkproof · cited by 62
- MeasureTheory.ae_restrict_of_aeproof · cited by 46
Cited by23
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_eq_zero_iff'proof · cited by 16
- MeasureTheory.withDensity_absolutelyContinuous'proof · cited by 5
- MeasureTheory.withDensity_mul₀proof · cited by 5
- MeasureTheory.measure_le_laverage_posproof · cited by 3
- MeasureTheory.withDensity_apply_eq_zero'proof · cited by 2
- MeasureTheory.ae_le_of_forall_setLIntegral_le_of_sigmaFinite₀proof · cited by 2
- MeasureTheory.setLIntegral_tilted'proof · cited by 2
- MeasureTheory.setLIntegral_trim_aeproof · cited by 2
- MeasureTheory.setIntegral_tilted'proof · cited by 2
- MeasureTheory.AEMeasurable.ae_eq_of_forall_setLIntegral_eqproof · cited by 2
- AEMeasurable.indicatorproof · cited by 2
- MeasureTheory.toReal_condLExpproof · cited by 2