Theorems · Theorem · probability

MeasureTheory.Adapted.isStoppingTime_hittingBtwn

∀ {Ω : Type u_1} {β : Type u_2} {ι : Type u_3} {m : MeasurableSpace Ω} [inst : ConditionallyCompleteLinearOrder ι]
  [WellFoundedLT ι] [Countable ι] {x : MeasurableSpace β} {f : MeasureTheory.Filtration ι m} {u : ι → Ω → β} {s : Set β}
  {n n' : ι},
  MeasureTheory.Adapted f u →
    MeasurableSet s → MeasureTheory.IsStoppingTime f fun ω => ↑(MeasureTheory.hittingBtwn u s n n' ω)

A discrete hitting time is a stopping time.

Defined in

Mathlib.Probability.Process.HittingTime

Cited by

5 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderWellFoundedLTCountable