Theorems · Theorem · probability

ProbabilityTheory.Kernel.ae_compProd_of_ae_ae

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {a : α} {κ : ProbabilityTheory.Kernel α β} {η : ProbabilityTheory.Kernel (α × β) γ}
  {p : β × γ → Prop},
  MeasurableSet {x | p x} → (∀ᵐ (b : β) ∂κ a, ∀ᵐ (c : γ) ∂η (a, b), p (b, c)) → ∀ᵐ (bc : β × γ) ∂(κ.compProd η) a, p bc

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

2 results in Mathlib

Foundations

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