Theorems · Theorem · probability

MeasureTheory.Measure.integrable_compProd_snd_iff

∀ {α : Type u_5} {β : Type u_6} {E : Type u_7} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  [inst : NormedAddCommGroup E] {κ : ProbabilityTheory.Kernel α β} {μ : MeasureTheory.Measure α} {f : β → E}
  [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ],
  MeasureTheory.AEStronglyMeasurable f (μ.bind ⇑κ) →
    (MeasureTheory.Integrable (fun p => f p.2) (μ.compProd κ) ↔ MeasureTheory.Integrable f (μ.bind ⇑κ))

Defined in

Mathlib.Probability.Kernel.Composition.IntegralCompProd

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupMeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel