Theorems · Theorem · probability

ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone

∀ {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)}
  [ProbabilityTheory.IsFiniteKernel κ] (a : α) (seq : ℕ → Set β),
  Monotone seq →
    ⋃ i, seq i = Set.univ →
      (∀ (m : ℕ), MeasurableSet (seq m)) →
        ∀ᵐ (x : γ) ∂κ.fst a, Filter.Tendsto (fun m => κ.density κ.fst a x (seq m)) Filter.atTop (nhds 1)

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

0 results in Mathlib

Foundations

Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGeneratedProbabilityTheory.IsFiniteKernel