Theorems · Theorem · probability

MeasureTheory.Measure.setLIntegral_compProd

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {κ : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ]
  {f : α × β → ENNReal},
  Measurable f →
    ∀ {s : Set α},
      MeasurableSet s →
        ∀ {t : Set β},
          MeasurableSet t →
            ∫⁻ (x : α × β) in s ×ˢ t, f x ∂μ.compProd κ = ∫⁻ (a : α) in s, ∫⁻ (b : β) in t, f (a, b) ∂κ a ∂μ

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

2 results in Mathlib

Foundations

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

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel