Theorems · Theorem · probability

MeasureTheory.Measure.setLIntegral_condKernel_univ_right

∀ {β : Type u_1} {Ω : Type u_2} {mβ : MeasurableSpace β} [inst : MeasurableSpace Ω] [inst_1 : StandardBorelSpace Ω]
  [inst_2 : Nonempty Ω] {ρ : MeasureTheory.Measure (β × Ω)} [inst_3 : MeasureTheory.IsFiniteMeasure ρ]
  {f : β × Ω → ENNReal},
  Measurable f →
    ∀ {s : Set β},
      MeasurableSet s →
        ∫⁻ (b : β) in s, ∫⁻ (ω : Ω), f (b, ω) ∂ρ.condKernel b ∂ρ.fst = ∫⁻ (x : β × Ω) in s ×ˢ Set.univ, f x ∂ρ

Defined in

Mathlib.Probability.Kernel.Disintegration.Integral

Cited by

0 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure