Theorems · Theorem · measure theory

MeasureTheory.AEEqFun.compMeasurable_mk

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α}
  [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace γ] [inst_3 : MeasurableSpace β]
  [inst_4 : TopologicalSpace.PseudoMetrizableSpace β] [inst_5 : BorelSpace β] [inst_6 : MeasurableSpace γ]
  [inst_7 : TopologicalSpace.PseudoMetrizableSpace γ] [inst_8 : OpensMeasurableSpace γ]
  [inst_9 : SecondCountableTopology γ] (g : β → γ) (hg : Measurable g) (f : α → β)
  (hf : MeasureTheory.AEStronglyMeasurable f μ),
  MeasureTheory.AEEqFun.compMeasurable g hg (MeasureTheory.AEEqFun.mk f hf) = MeasureTheory.AEEqFun.mk (g ∘ f) ⋯

Defined in

Mathlib.MeasureTheory.Function.AEEqFun

Cited by

2 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpaceMeasurableSpaceTopologicalSpace.PseudoMetrizableSpaceBorelSpaceMeasurableSpaceTopologicalSpace.PseudoMetrizableSpaceOpensMeasurableSpaceSecondCountableTopology