Theorems · Theorem · probability

ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_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} {β : Type u_4}
  {p : Set ι → Prop} {f : Filter ι} {ns : β → Set ι},
  (∀ (n : ι), s n ≤ m0) →
    ProbabilityTheory.Kernel.iIndep s κ μα →
      (∀ (t : Set ι), p t → tᶜ ∈ f) →
        Directed (fun x1 x2 => x1 ⊆ x2) ns →
          (∀ (a : β), p (ns a)) →
            (∀ (n : ι), ∃ a, n ∈ ns a) → ∀ {t : Set Ω}, MeasurableSet t → ∀ᵐ (a : α) ∂μα, (κ a) t = 0 ∨ (κ a) t = 1

Defined in

Mathlib.Probability.Independence.ZeroOne

Cited by

2 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound