Theorems · Theorem · probability
MeasureTheory.StronglyAdapted.isStoppingTime_upperCrossingTime
∀ {Ω : Type u_1} {m0 : MeasurableSpace Ω} {a b : ℝ} {f : ℕ → Ω → ℝ} {N n : ℕ} {ℱ : MeasureTheory.Filtration ℕ m0},
MeasureTheory.StronglyAdapted ℱ f →
MeasureTheory.IsStoppingTime ℱ fun ω => ↑(MeasureTheory.upperCrossingTime a b f N n ω)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- WithTopstatement · cited by 3,754
- MeasureTheory.Filtrationstatement and proof · cited by 425
- MeasureTheory.IsStoppingTimestatement · cited by 122
- MeasureTheory.StronglyAdaptedstatement and proof · cited by 81
- MeasureTheory.upperCrossingTimestatement · cited by 42
- MeasureTheory.StronglyAdapted.isStoppingTime_crossingproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyAdapted.measurable_upcrossingsBeforeproof · cited by 3
- MeasureTheory.StronglyAdapted.upcrossingStratproof · cited by 2