Theorems · Theorem · probability

ProbabilityTheory.Kernel.eq_rnDeriv

∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {κ η : ProbabilityTheory.Kernel α γ}
  [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] {ξ : ProbabilityTheory.Kernel α γ} {f : α → γ → ENNReal}
  [inst : ProbabilityTheory.IsFiniteKernel η] [ProbabilityTheory.IsFiniteKernel κ],
  κ = η.withDensity f + ξ →
    Measurable (Function.uncurry f) → ∀ (a : α), (ξ a).MutuallySingular (η a) → f a =ᵐ[η a] κ.rnDeriv η a

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

0 results in Mathlib

Foundations

Depth 334 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel