Theorems · Theorem · probability

ProbabilityTheory.Kernel.ae_kernel_lt_top

∀ {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)} {κ : ProbabilityTheory.Kernel α β} [ProbabilityTheory.IsSFiniteKernel κ]
  {η : ProbabilityTheory.Kernel (α × β) γ} [ProbabilityTheory.IsSFiniteKernel η] (a : α),
  ((κ.compProd η) a) s ≠ ⊤ → ∀ᵐ (b : β) ∂κ a, (η (a, b)) (Prod.mk b ⁻¹' s) < ⊤

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

2 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel