Theorems · Theorem · probability

ProbabilityTheory.Locally.of_and

∀ {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 : TopologicalSpace ι] [inst_3 : OrderTopology ι] [inst_4 : Zero E],
  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

3 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderOrderBotTopologicalSpaceOrderTopologyZero