Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_congr

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

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