Theorems · Theorem · probability

ProbabilityTheory.Kernel.prod_apply_prod

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {κ : ProbabilityTheory.Kernel α β} {η : ProbabilityTheory.Kernel α γ}
  [ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsSFiniteKernel η] {s : Set β} {t : Set γ} {a : α},
  ((κ.prod η) a) (s ×ˢ t) = (κ a) s * (η a) t

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

4 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel