Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_parallelComp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {mδ : MeasurableSpace δ} {κ : ProbabilityTheory.Kernel α β}
  {η : ProbabilityTheory.Kernel γ δ} [ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsSFiniteKernel η]
  (ac : α × γ) {g : β × δ → ENNReal},
  Measurable g → ∫⁻ (bd : β × δ), g bd ∂(κ.parallelComp η) ac = ∫⁻ (b : β), ∫⁻ (d : δ), g (b, d) ∂η ac.2 ∂κ ac.1

Defined in

Mathlib.Probability.Kernel.Composition.ParallelComp

Cited by

0 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel