Theorems · Theorem · probability
MeasureTheory.upcrossingsBefore_eq_sum
∀ {Ω : Type u_1} {a b : ℝ} {f : ℕ → Ω → ℝ} {N : ℕ} {ω : Ω},
a < b →
MeasureTheory.upcrossingsBefore a b f N ω =
∑ i ∈ Finset.Ico 1 (N + 1), {n | MeasureTheory.upperCrossingTime a b f N n ω < N}.indicator 1 i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.ofPredstatement and proof · cited by 6,101
- Finset.sumstatement and proof · cited by 5,195
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- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Set.indicatorstatement and proof · cited by 723
- Eq.leproof · cited by 605
- Finset.Icostatement and proof · cited by 450
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyAdapted.measurable_upcrossingsBeforeproof · cited by 3