Theorems · Theorem · probability

MeasureTheory.Measure.integrable_comp_iff

∀ {α : Type u_1} {β : Type u_2} {E : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  [inst : NormedAddCommGroup E] {κ : ProbabilityTheory.Kernel α β} {μ : MeasureTheory.Measure α} {f : β → E},
  MeasureTheory.AEStronglyMeasurable f (μ.bind ⇑κ) →
    (MeasureTheory.Integrable f (μ.bind ⇑κ) ↔
      (∀ᵐ (x : α) ∂μ, MeasureTheory.Integrable f (κ x)) ∧ MeasureTheory.Integrable (fun x => ∫ (y : β), ‖f y‖ ∂κ x) μ)

Defined in

Mathlib.Probability.Kernel.Composition.IntegralCompProd

Cited by

0 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup