(First) If Σ P(A_n) < ∞ then almost surely only finitely many of the A_n occur. (Second) If the A_n are independent and Σ P(A_n) = ∞ then almost surely infinitely many occur. Zero-one characterisation of limsup events. Borel 1909,…
(First) If Σ P(A_n) < ∞ then almost surely only finitely many of the A_n occur. (Second) If the A_n are independent and Σ P(A_n) = ∞ then almost surely infinitely many occur. Zero-one characterisation of limsup events. Borel 1909,…