Theorems · Theorem · probability

ProbabilityTheory.Kernel.comap_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 β γ)
  [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel β δ) [ProbabilityTheory.IsSFiniteKernel η]
  {f : α → β} (hf : Measurable f), (κ.prod η).comap f hf = (κ.comap f hf).prod (η.comap f hf)

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

1 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel