Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_restrict

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {s : Set β}
  (κ : ProbabilityTheory.Kernel α β) (hs : MeasurableSet s) (a : α) (f : β → ENNReal),
  ∫⁻ (b : β), f b ∂(κ.restrict hs) a = ∫⁻ (b : β) in s, f b ∂κ a

Defined in

Mathlib.Probability.Kernel.Basic

Cited by

2 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound