Theorems · Theorem · measure theory

MeasureTheory.Measure.map_map

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {μ : MeasureTheory.Measure α} {g : β → γ} {f : α → β},
  Measurable g →
    Measurable f → MeasureTheory.Measure.map g (MeasureTheory.Measure.map f μ) = MeasureTheory.Measure.map (g ∘ f) μ

Mapping a measure twice is the same as mapping the measure with the composition. This version is for measurable functions. See map_map_of_aemeasurable when they are just ae measurable.

Defined in

Mathlib.MeasureTheory.Measure.Map

Cited by

67 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound