Theorems · Theorem · probability

MeasureTheory.IsStoppingTime.measurableSet_lt_of_isLUB

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

Auxiliary lemma for MeasureTheory.IsStoppingTime.measurableSet_lt.

Defined in

Mathlib.Probability.Process.Stopping

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyFirstCountableTopology