Theorems · Theorem · probability

ProbabilityTheory.IsStable.locally_and_iff

∀ {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 q : (ι → Ω → E) → Prop}
  [inst_1 : OrderBot ι] [inst_2 : Zero E] [inst_3 : TopologicalSpace ι] [inst_4 : OrderTopology ι],
  ProbabilityTheory.IsStable 𝓕 p →
    ProbabilityTheory.IsStable 𝓕 q →
      (ProbabilityTheory.Locally (fun Y => p Y ∧ q Y) 𝓕 X P ↔
        ProbabilityTheory.Locally p 𝓕 X P ∧ ProbabilityTheory.Locally q 𝓕 X P)

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

1 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderOrderBotZeroTopologicalSpaceOrderTopology