Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_apply

∀ {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), (κ.withDensity f) a = (κ a).withDensity (f a)

Defined in

Mathlib.Probability.Kernel.WithDensity

Cited by

15 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernel