Theorems · Theorem · probability

MeasureTheory.Measure.compProd_assoc

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {κ : ProbabilityTheory.Kernel α β} {γ : Type u_3} {mγ : MeasurableSpace γ} {η : ProbabilityTheory.Kernel (α × β) γ},
  MeasureTheory.Measure.map (⇑MeasurableEquiv.prodAssoc.symm) (μ.compProd (κ.compProd η)) = (μ.compProd κ).compProd η

Measure.compProd is associative. We have to insert MeasurableEquiv.prodAssoc because the products of types α × β × γ and (α × β) × γ are different.

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

1 results in Mathlib

Foundations

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