Theorems · Theorem · probability

MeasureTheory.Measure.compProd_apply

∀ {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] {s : Set (α × β)},
  MeasurableSet s → (μ.compProd κ) s = ∫⁻ (a : α), (κ a) (Prod.mk a ⁻¹' s) ∂μ

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

18 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel