Theorems · Theorem · probability

ProbabilityTheory.IsLocalizingSequence.isPrelocalizingSequence_inf_extraction

∀ {ι : Type u_1} {Ω : Type u_2} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω}
  [inst : ConditionallyCompleteLinearOrderBot ι] [inst_1 : TopologicalSpace ι] [inst_2 : OrderTopology ι]
  {𝓕 : MeasureTheory.Filtration ι mΩ} [SecondCountableTopology ι] [MeasureTheory.IsFiniteMeasure P] [NoMaxOrder ι]
  {τ : ℕ → Ω → WithTop ι} {σ : ℕ → ℕ → Ω → WithTop ι},
  ProbabilityTheory.IsLocalizingSequence 𝓕 τ P →
    (∀ (n : ℕ), ProbabilityTheory.IsLocalizingSequence 𝓕 (σ n) P) →
      ∃ nk, StrictMono nk ∧ ProbabilityTheory.IsPreLocalizingSequence 𝓕 (fun i ω => min (τ i ω) (σ i (nk i) ω)) P

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

1 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderBotTopologicalSpaceOrderTopologySecondCountableTopologyMeasureTheory.IsFiniteMeasureNoMaxOrder