Theorems · Theorem · probability

ProbabilityTheory.Kernel.map_prod_map

∀ {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} {ε : Type u_6} {mε : MeasurableSpace ε}
  (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel α δ)
  [ProbabilityTheory.IsSFiniteKernel η] {f : β → γ},
  Measurable f → ∀ {g : δ → ε}, Measurable g → (κ.map f).prod (η.map g) = (κ.prod η).map (Prod.map f g)

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

4 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel