Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.biInf

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : ConditionallyCompleteLinearOrderBot ι]
  [inst_1 : TopologicalSpace ι] [OrderTopology ι] [DenselyOrdered ι] [FirstCountableTopology ι] [NoMaxOrder ι]
  {κ : Type u_4} {f : MeasureTheory.Filtration ι m} {τ : κ → Ω → WithTop ι} {s : Set κ},
  s.Countable →
    ∀ [f.IsRightContinuous],
      (∀ n ∈ s, MeasureTheory.IsStoppingTime f (τ n)) → MeasureTheory.IsStoppingTime f fun ω => ⨅ n ∈ s, τ n ω

Defined in

Mathlib.Probability.Process.Stopping

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderBotTopologicalSpaceOrderTopologyDenselyOrderedFirstCountableTopologyNoMaxOrderMeasureTheory.Filtration.IsRightContinuous