Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.comp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μa : MeasureTheory.Measure α} {μb : MeasureTheory.Measure β}
  {μc : MeasureTheory.Measure γ} {g : β → γ} {f : α → β},
  MeasureTheory.MeasurePreserving g μb μc →
    MeasureTheory.MeasurePreserving f μa μb → MeasureTheory.MeasurePreserving (g ∘ f) μa μc

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

40 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpace