Mathlib Map

Theorems · Definition · probability

MeasureTheory.upcrossingsBefore

{Ω : Type u_1} → {ι : Type u_2} → [inst : Preorder ι] → [OrderBot ι] → [InfSet ι] → ℝ → ℝ → (ι → Ω → ℝ) → ι → Ω → ℕ

The number of upcrossings (strictly) before time N.

Defined in
Mathlib.Probability.Martingale.Upcrossing
Cited by
22 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderOrderBotInfSet

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.upcrossings · cited by 9MeasureTheory.upcrossingsMeasureTheory.upcrossingsBefore_zero · cited by 3MeasureTheory.upcrossings…MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBefore · cited by 3MeasureTheory.upperCrossi…MeasureTheory.StronglyAdapted.measurable_upcrossingsBefore · cited by 3StronglyAdapted.measurabl…MeasureTheory.upcrossingsBefore_le · cited by 3MeasureTheory.upcrossings…MeasureTheory.upcrossingsBefore_zero' · cited by 2MeasureTheory.upcrossings…MeasureTheory.upperCrossingTime_eq_of_upcrossingsBefore_lt · cited by 2MeasureTheory.upperCrossi…MeasureTheory.not_frequently_of_upcrossings_lt_top · cited by 2MeasureTheory.not_frequen…MeasureTheory.upcrossingsBefore_lt_of_exists_upcrossing · cited by 1MeasureTheory.upcrossings…MeasureTheory.upcrossingsBefore_mono · cited by 1MeasureTheory.upcrossings…MeasureTheory.upcrossingsBefore_pos_eq · cited by 1MeasureTheory.upcrossings…MeasureTheory.upcrossings_lt_top_iff · cited by 1MeasureTheory.upcrossings…MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part · cited by 1Submartingale.mul_integra…MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part · cited by 1Submartingale.mul_lintegr…MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt · cited by 1MeasureTheory.sub_eq_zero…Real · cited by 25697RealPreorder · cited by 7952PreorderSet.ofPred · cited by 6101Set.ofPredOrderBot · cited by 1055OrderBotSupSet.sSup · cited by 954SupSet.sSupInfSet · cited by 145InfSetMeasureTheory.upperCrossingTime · cited by 42MeasureTheory.upperCrossi…MeasureTheory.upcrossingsBefo…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.