=+4.11.

(a) If A1, A2 ,... are independent events, then P(("- ¡ A,)= IIm_ P(A,) and P(U",A.)=1-IT ;_; (1-P(A)). Prove these facts and from them derive the second Borel-Cantelli lemma by the well-known relation between infinite

· series and products.