Theorems · Theorem · probability

ProbabilityTheory.Kernel.prod_const_comp

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {δ : Type u_6} {mδ : MeasurableSpace δ} (κ : ProbabilityTheory.Kernel α β)
  [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel β γ) [ProbabilityTheory.IsSFiniteKernel η]
  (μ : MeasureTheory.Measure δ) [MeasureTheory.SFinite μ],
  (η.prod (ProbabilityTheory.Kernel.const β μ)).comp κ = (η.comp κ).prod (ProbabilityTheory.Kernel.const α μ)

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

1 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernelMeasureTheory.SFinite