Theorems · Theorem · probability

ProbabilityTheory.Kernel.indep_biSup_limsup

∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {_mα : MeasurableSpace α} {s : ι → MeasurableSpace Ω}
  {m0 : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω} {μα : MeasureTheory.Measure α} {p : Set ι → Prop}
  {f : Filter ι},
  (∀ (n : ι), s n ≤ m0) →
    ProbabilityTheory.Kernel.iIndep s κ μα →
      (∀ (t : Set ι), p t → tᶜ ∈ f) →
        ∀ {t : Set ι}, p t → ProbabilityTheory.Kernel.Indep (⨆ n ∈ t, s n) (Filter.limsup s f) κ μα

Defined in

Mathlib.Probability.Independence.ZeroOne

Cited by

3 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound