Theorems · Theorem · probability

MeasureTheory.Measure.prod_comp_right

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν]
  {κ : ProbabilityTheory.Kernel β γ} [ProbabilityTheory.IsSFiniteKernel κ],
  μ.prod (ν.bind ⇑κ) = (μ.prod ν).bind ⇑(ProbabilityTheory.Kernel.id.parallelComp κ)

Defined in

Mathlib.Probability.Kernel.Composition.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel