theorem
second_Borel_Cantelli
{Ω : Type u_1}
{m0 : MeasurableSpace Ω}
{μ : MeasureTheory.Measure Ω}
{A : ℕ → Set Ω}
(hm : ∀ (n : ℕ), MeasurableSet (A n))
(hindep : ProbabilityTheory.iIndepSet A μ)
(hsum : ∑' (n : ℕ), μ (A n) = ⊤)
:
Second Borel–Cantelli lemma. If the events Aₙ are (mutually) independent
and ∑ₙ μ(Aₙ) = ∞, then almost every point belongs to infinitely many of the
Aₙ, i.e. μ(limsup Aₙ) = 1.