Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_apply_univ

∀ {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.IsMarkovKernel η] {a : α},
  ((κ.compProd η) a) Set.univ = (κ a) Set.univ

Defined in

Mathlib.Probability.Kernel.Composition.CompProd

Cited by

1 results in Mathlib

Foundations

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

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsMarkovKernel