Theorems · Theorem · probability

MeasureTheory.Measure.prodMkLeft_comp_compProd

∀ {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} {κ : ProbabilityTheory.Kernel α β}
  {η : ProbabilityTheory.Kernel β γ} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ],
  (μ.compProd κ).bind ⇑(ProbabilityTheory.Kernel.prodMkLeft α η) = (μ.bind ⇑κ).bind ⇑η

Defined in

Mathlib.Probability.Kernel.Composition.MeasureComp

Cited by

1 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel