Theorems · Theorem · probability

MeasureTheory.supermartingale_of_setIntegral_succ_le

∀ {Ω : Type u_1} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {𝒢 : MeasureTheory.Filtration ℕ m0}
  [MeasureTheory.IsFiniteMeasure μ] {f : ℕ → Ω → ℝ},
  MeasureTheory.StronglyAdapted 𝒢 f →
    (∀ (i : ℕ), MeasureTheory.Integrable (f i) μ) →
      (∀ (i : ℕ) (s : Set Ω), MeasurableSet s → ∫ (ω : Ω) in s, f (i + 1) ω ∂μ ≤ ∫ (ω : Ω) in s, f i ω ∂μ) →
        MeasureTheory.Supermartingale f 𝒢 μ

Defined in

Mathlib.Probability.Martingale.Basic

Cited by

0 results in Mathlib

Foundations

Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasure