Theorems · Theorem · probability

ProbabilityTheory.Locally.mono

∀ {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],
  (∀ (X : ι → Ω → E), p X → q X) → ProbabilityTheory.Locally p 𝓕 X P → ProbabilityTheory.Locally q 𝓕 X P

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderOrderBotTopologicalSpaceOrderTopologyZero