Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_prod

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ]
  (η : ProbabilityTheory.Kernel α γ) [ProbabilityTheory.IsSFiniteKernel η] (a : α) {g : β × γ → ENNReal},
  Measurable g → ∫⁻ (c : β × γ), g c ∂(κ.prod η) a = ∫⁻ (b : β), ∫⁻ (c : γ), g (b, c) ∂η a ∂κ a

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

3 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel