Theorems · Theorem · probability

MeasureTheory.stoppedValue_upperCrossingTime

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

Defined in

Mathlib.Probability.Martingale.Upcrossing

Cited by

3 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound