Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_compProd

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ]
  (η : ProbabilityTheory.Kernel (α × β) γ) [ProbabilityTheory.IsSFiniteKernel η] (a : α) {f : β × γ → ENNReal},
  Measurable f → ∫⁻ (bc : β × γ), f bc ∂(κ.compProd η) a = ∫⁻ (b : β), ∫⁻ (c : γ), f (b, c) ∂η (a, b) ∂κ a

Lebesgue integral against the composition-product of two kernels.

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

7 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel