Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_apply

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {s : Set (β × γ)},
  MeasurableSet s →
    ∀ (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel (α × β) γ)
      [ProbabilityTheory.IsSFiniteKernel η] (a : α),
      ((κ.compProd η) a) s = ∫⁻ (b : β), (η (a, b)) (Prod.mk b ⁻¹' s) ∂κ a

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

31 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel