Theorems · Theorem · measure theory

AEMeasurable.map_map_of_aemeasurable

∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} {m0 : MeasurableSpace α} [inst : MeasurableSpace β]
  [inst_1 : MeasurableSpace γ] {μ : MeasureTheory.Measure α} {g : β → γ} {f : α → β},
  AEMeasurable g (MeasureTheory.Measure.map f μ) →
    AEMeasurable f μ → MeasureTheory.Measure.map g (MeasureTheory.Measure.map f μ) = MeasureTheory.Measure.map (g ∘ f) μ

Defined in

Mathlib.MeasureTheory.Measure.AEMeasurable

Cited by

28 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace