Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_eq_zero_iff

∀ {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} {η : ProbabilityTheory.Kernel (α × β) γ}
  [ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsSFiniteKernel η],
  κ.compProd η = 0 ↔ ∀ (a : α), ∀ᵐ (b : β) ∂κ a, η (a, b) = 0

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

0 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel