Theorems · Theorem · probability

ProbabilityTheory.Kernel.rnDeriv_withDensity

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