Theorems · Theorem · probability

ProbabilityTheory.Kernel.stronglyAdapted_densityProcess

∀ {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) (a : α) {s : Set β},
  MeasurableSet s →
    MeasureTheory.StronglyAdapted (ProbabilityTheory.countableFiltration γ) fun n x => κ.densityProcess ν n a x s

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

1 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGenerated