Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_sum_left

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {ι : Type u_4} [inst : Countable ι] {κ : ι → ProbabilityTheory.Kernel α β}
  {η : ProbabilityTheory.Kernel (α × β) γ} [∀ (i : ι), ProbabilityTheory.IsSFiniteKernel (κ i)],
  (ProbabilityTheory.Kernel.sum κ).compProd η = ProbabilityTheory.Kernel.sum fun i => (κ i).compProd η

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

CountableProbabilityTheory.IsSFiniteKernel