Theorems · Theorem · probability
MeasureTheory.upperCrossingTime_le_lowerCrossingTime
∀ {Ω : Type u_1} {ι : Type u_2} [inst : ConditionallyCompleteLinearOrderBot ι] {a b : ℝ} {f : ι → Ω → ℝ} {N : ι} {n : ℕ}
{ω : Ω}, MeasureTheory.upperCrossingTime a b f N n ω ≤ MeasureTheory.lowerCrossingTime a b f N n ω- Cited by
- 7 results in Mathlib
- Foundations
- Depth 108 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.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Iicproof · cited by 1,111
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- MeasureTheory.upperCrossingTimestatement · cited by 42
- MeasureTheory.lowerCrossingTimestatement · cited by 23
- MeasureTheory.upperCrossingTime_leproof · cited by 10
- MeasureTheory.le_hittingBtwnproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.upperCrossingTime_monoproof · cited by 5
- MeasureTheory.lowerCrossingTime_monoproof · cited by 3
- MeasureTheory.upperCrossingTime_lt_succproof · cited by 2
- MeasureTheory.crossing_eq_crossing_of_lowerCrossingTime_ltproof · cited by 1
- MeasureTheory.upcrossingStrat_le_oneproof · cited by 1
- MeasureTheory.sub_eq_zero_of_upcrossingsBefore_ltproof · cited by 1
- MeasureTheory.upperCrossingTime_lt_lowerCrossingTimeproof · cited by 0