Theorems · Theorem · probability

ProbabilityTheory.condIndep_limsup_atTop_self

∀ {Ω : Type u_2} {ι : Type u_3} {s : ι → MeasurableSpace Ω} {m m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω}
  [inst : SemilatticeSup ι] [NoMaxOrder ι] [Nonempty ι] [inst_3 : StandardBorelSpace Ω] (hm : m ≤ m0)
  [inst_4 : MeasureTheory.IsFiniteMeasure μ],
  (∀ (n : ι), s n ≤ m0) →
    ProbabilityTheory.iCondIndep m hm s μ →
      ProbabilityTheory.CondIndep m (Filter.limsup s Filter.atTop) (Filter.limsup s Filter.atTop) hm μ

Defined in

Mathlib.Probability.Independence.ZeroOne

Cited by

1 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupNoMaxOrderNonemptyStandardBorelSpaceMeasureTheory.IsFiniteMeasure