Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_withDensity

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α → β → ENNReal}
  (κ : ProbabilityTheory.Kernel α β) [inst : ProbabilityTheory.IsSFiniteKernel κ],
  Measurable (Function.uncurry f) →
    ∀ (a : α) {g : β → ENNReal}, Measurable g → ∫⁻ (b : β), g b ∂(κ.withDensity f) a = ∫⁻ (b : β), f a b * g b ∂κ a

Defined in

Mathlib.Probability.Kernel.WithDensity

Cited by

0 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernel