Theorems · Theorem · probability

ProbabilityTheory.lintegral_condKernel_mem

∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  [inst : MeasurableSpace Ω] [inst_1 : StandardBorelSpace Ω] [inst_2 : Nonempty Ω]
  [inst_3 : MeasurableSpace.CountableOrCountablyGenerated α β] {κ : ProbabilityTheory.Kernel α (β × Ω)}
  [inst_4 : ProbabilityTheory.IsFiniteKernel κ] (a : α) {s : Set (β × Ω)},
  MeasurableSet s → ∫⁻ (x : β), (κ.condKernel (a, x)) (Prod.mk x ⁻¹' s) ∂κ.fst a = (κ a) s

Defined in

Mathlib.Probability.Kernel.Disintegration.Integral

Cited by

0 results in Mathlib

Foundations

Depth 338 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernel