Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_compl_mutuallySingularSetSlice

∀ {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] [ProbabilityTheory.IsFiniteKernel κ]
  [inst : ProbabilityTheory.IsFiniteKernel η] {a : α} {s : Set γ},
  MeasurableSet s → s ⊆ (κ.mutuallySingularSetSlice η a)ᶜ → ((η.withDensity (κ.rnDeriv η)) a) s = (κ a) s

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 329 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel