Theorems · Theorem · probability

ProbabilityTheory.Locally.stoppedProcess_localSeq

∀ {ι : Type u_1} {Ω : Type u_2} {E : Type u_3} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω}
  [inst : LinearOrder ι] {𝓕 : MeasureTheory.Filtration ι mΩ} {X : ι → Ω → E} {p : (ι → Ω → E) → Prop}
  [inst_1 : OrderBot ι] [inst_2 : TopologicalSpace ι] [inst_3 : OrderTopology ι] [inst_4 : Zero E]
  (hX : ProbabilityTheory.Locally p 𝓕 X P) (n : ℕ),
  p (MeasureTheory.stoppedProcess (fun i => {ω | ⊥ < hX.localSeq n ω}.indicator (X i)) (hX.localSeq n))

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

4 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderOrderBotTopologicalSpaceOrderTopologyZero