Theorems · Theorem · probability

ProbabilityTheory.Kernel.map_prod_eq

∀ {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]
  {f : β → δ}, Measurable f → (κ.map f).prod η = (κ.prod η).map (Prod.map f id)

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

1 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel