Theorems · Theorem · probability

MeasureTheory.isStoppingTime_of_measurableSet_lt_of_isRightContinuous

∀ {Ω : Type u_1} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : ConditionallyCompleteLinearOrder ι]
  [inst_1 : TopologicalSpace ι] [OrderTopology ι] [FirstCountableTopology ι] {f : MeasureTheory.Filtration ι m}
  [DenselyOrdered ι] [NoMaxOrder ι] {τ : Ω → WithTop ι} [f.IsRightContinuous],
  (∀ (i : ι), MeasurableSet {ω | τ ω < ↑i}) → MeasureTheory.IsStoppingTime f τ

Defined in

Mathlib.Probability.Process.Stopping

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFirstCountableTopologyDenselyOrderedNoMaxOrderMeasureTheory.Filtration.IsRightContinuous