Theorems · Theorem · probability

ProbabilityTheory.Kernel.prodAssoc_prod

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4} {δ : Type u_5}
  {mγ : MeasurableSpace γ} {mδ : MeasurableSpace δ} (κ : ProbabilityTheory.Kernel α β)
  [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel α γ) [ProbabilityTheory.IsSFiniteKernel η]
  (ξ : ProbabilityTheory.Kernel α δ) [ProbabilityTheory.IsSFiniteKernel ξ],
  ((κ.prod ξ).prod η).map ⇑MeasurableEquiv.prodAssoc = κ.prod (ξ.prod η)

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

2 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel