Theorems · Theorem · probability

ProbabilityTheory.HasIndepIncrements.of_nat

∀ {T : Type u_1} {Ω : Type u_2} {E : Type u_3} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {X : T → Ω → E}
  [inst : Preorder T] [inst_1 : MeasurableSpace E] [inst_2 : Sub E],
  (∀ (t : ℕ → T),
      Monotone t →
        Filter.EventuallyConst t Filter.atTop →
          ProbabilityTheory.iIndepFun (fun i ω => X (t (i + 1)) ω - X (t i) ω) P) →
    ProbabilityTheory.HasIndepIncrements X P

Defined in

Mathlib.Probability.Independence.Process.HasIndepIncrements.Basic

Cited by

1 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderMeasurableSpaceSub