Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_restrict

∀ {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} [ProbabilityTheory.IsSFiniteKernel κ]
  {η : ProbabilityTheory.Kernel (α × β) γ} [ProbabilityTheory.IsSFiniteKernel η] {s : Set β} {t : Set γ}
  (hs : MeasurableSet s) (ht : MeasurableSet t), (κ.restrict hs).compProd (η.restrict ht) = (κ.compProd η).restrict ⋯

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

4 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel