Theorems · Theorem · probability

MeasureTheory.le_sub_of_le_upcrossingsBefore

∀ {Ω : Type u_1} {a b : ℝ} {f : ℕ → Ω → ℝ} {N n : ℕ} {ω : Ω},
  0 < N →
    a < b →
      n < MeasureTheory.upcrossingsBefore a b f N ω →
        b - a ≤
          MeasureTheory.stoppedValue f (fun ω => ↑(MeasureTheory.upperCrossingTime a b f N (n + 1) ω)) ω -
            MeasureTheory.stoppedValue f (fun ω => ↑(MeasureTheory.lowerCrossingTime a b f N n ω)) ω

Defined in

Mathlib.Probability.Martingale.Upcrossing

Cited by

1 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound