Theorems · Theorem · probability

ProbabilityTheory.Kernel.lintegral_rnDeriv

∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
  [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] {κ η : ProbabilityTheory.Kernel α γ}
  [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η] {a : α},
  (κ a).AbsolutelyContinuous (η a) → ∫⁻ (c : γ), κ.rnDeriv η a c ∂η a = (κ a) Set.univ

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

0 results in Mathlib

Foundations

Depth 335 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel