Theorems · Theorem · probability

ProbabilityTheory.Kernel.ae_ae_of_ae_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} {p : β × γ → Prop},
  (∀ᵐ (bc : β × γ) ∂(κ.compProd η) a, p bc) → ∀ᵐ (b : β) ∂κ a, ∀ᵐ (c : γ) ∂η (a, b), p (b, c)

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

7 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel