Theorems · Theorem · probability

ProbabilityTheory.Kernel.tendsto_m_density

∀ {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},
  κ.fst ≤ ν →
    ∀ (a : α) [ProbabilityTheory.IsFiniteKernel ν] {s : Set β},
      MeasurableSet s →
        ∀ᵐ (x : γ) ∂ν a, Filter.Tendsto (fun n => κ.densityProcess ν n a x s) Filter.atTop (nhds (κ.density ν a x s))

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

0 results in Mathlib

Foundations

Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGeneratedProbabilityTheory.IsFiniteKernel