Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_map

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {f : β → γ} (κ : ProbabilityTheory.Kernel α β),
  Measurable f → ∀ (a : α) {g' : γ → ENNReal}, Measurable g' → ∫⁻ (b : γ), g' b ∂(κ.map f) a = ∫⁻ (a : β), g' (f a) ∂κ a

Defined in

Mathlib.Probability.Kernel.Composition.MapComap

Cited by

8 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound