Theorems · Theorem · probability
MeasureTheory.upcrossings_lt_top_iff
∀ {Ω : Type u_1} {a b : ℝ} {f : ℕ → Ω → ℝ} {ω : Ω},
MeasureTheory.upcrossings a b f ω < ⊤ ↔ ∃ k, ∀ (N : ℕ), MeasureTheory.upcrossingsBefore a b f N ω ≤ k- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- LE.le.transproof · cited by 3,151
- le_rflproof · cited by 1,558
- ENNReal.ofNNRealproof · cited by 1,279
- LT.lt.neproof · cited by 872
- lt_of_le_of_ltproof · cited by 432
- Nat.cast_leproof · cited by 159
- ENNReal.coe_le_coeproof · cited by 73
- ENNReal.coe_lt_topproof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.not_frequently_of_upcrossings_lt_topproof · cited by 2