Theorems · Theorem · probability

ProbabilityTheory.IsPreLocalizingSequence.isLocalizingSequence_biInf

∀ {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} [DenselyOrdered ι] [FirstCountableTopology ι] [NoMaxOrder ι]
  {τ : ℕ → Ω → WithTop ι} [𝓕.IsRightContinuous],
  ProbabilityTheory.IsPreLocalizingSequence 𝓕 τ P →
    ProbabilityTheory.IsLocalizingSequence 𝓕 (fun i ω => ⨅ j, ⨅ (_ : j ≥ i), τ j ω) P

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderBotTopologicalSpaceOrderTopologyDenselyOrderedFirstCountableTopologyNoMaxOrderMeasureTheory.Filtration.IsRightContinuous