Theorems · Theorem · probability

MeasureTheory.Measure.compProd_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} {κ : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ]
  [ProbabilityTheory.IsSFiniteKernel κ] {f : β → γ},
  Measurable f → μ.compProd (κ.map f) = MeasureTheory.Measure.map (Prod.map id f) (μ.compProd κ)

Defined in

Mathlib.Probability.Kernel.Composition.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel