Theorems · Theorem · measure theory
MeasureTheory.ae_eq_comp
∀ {α : Type u_2} {β : Type u_3} {δ : Type u_4} {m0 : MeasurableSpace α} [inst : MeasurableSpace β]
{μ : MeasureTheory.Measure α} {f : α → β} {g g' : β → δ},
AEMeasurable f μ → g =ᵐ[MeasureTheory.Measure.map f μ] g' → g ∘ f =ᵐ[μ] g' ∘ f- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 203 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.Measure.AbsolutelyContinuous.rflproof · cited by 30
- MeasureTheory.ae_eq_comp'proof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_mapproof · cited by 67
- MeasureTheory.lintegral_map'proof · cited by 14
- AEMeasurable.comp_aemeasurableproof · cited by 9
- MeasureTheory.AEStronglyMeasurable.comp_aemeasurableproof · cited by 8
- essSup_map_measureproof · cited by 3
- MeasureTheory.AEStronglyMeasurable.comp_ae_measurable'proof · cited by 2
- ProbabilityTheory.indepFun_prod₀proof · cited by 2