Theorems · Theorem · probability

ProbabilityTheory.Kernel.parallelComp_apply

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {mδ : MeasurableSpace δ} (κ : ProbabilityTheory.Kernel α β)
  [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel γ δ) [ProbabilityTheory.IsSFiniteKernel η]
  (x : α × γ), (κ.parallelComp η) x = (κ x.1).prod (η x.2)

Defined in

Mathlib.Probability.Kernel.Composition.ParallelComp

Cited by

18 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernelProbabilityTheory.IsSFiniteKernel