Theorems · Theorem · probability

ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atTop

∀ {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} [inst : SemilatticeSup ι]
  [NoMaxOrder ι] [Nonempty ι],
  (∀ (n : ι), s n ≤ m0) →
    ProbabilityTheory.Kernel.iIndep s κ μα → ∀ {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

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupNoMaxOrderNonempty