Theorems · Theorem · probability

MeasureTheory.Measure.ae_ae_of_ae_compProd

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {κ : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ] {p : α × β → Prop},
  (∀ᵐ (x : α × β) ∂μ.compProd κ, p x) → ∀ᵐ (a : α) ∂μ, ∀ᵐ (b : β) ∂κ a, p (a, b)

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

3 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel