Theorems · Theorem · probability

ProbabilityTheory.Kernel.measurable_densityProcess_countableFiltration_aux

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} [inst : MeasurableSpace.CountablyGenerated γ] (κ : ProbabilityTheory.Kernel α (γ × β))
  (ν : ProbabilityTheory.Kernel α γ) (n : ℕ) {s : Set β},
  MeasurableSet s →
    Measurable fun p =>
      (κ p.1) (MeasurableSpace.countablePartitionSet n p.2 ×ˢ s) / (ν p.1) (MeasurableSpace.countablePartitionSet n p.2)

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

2 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGenerated