Theorems · Theorem · measure theory

Continuous.comp_aestronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace β] [inst_1 : TopologicalSpace γ]
  {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {g : β → γ} {f : α → β},
  Continuous g → MeasureTheory.AEStronglyMeasurable f μ → MeasureTheory.AEStronglyMeasurable (fun x => g (f x)) μ

The composition of a continuous function and an ae strongly measurable function is ae strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

77 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace