Let{A1, A2, A3,...} be a sequence of events. Prove that if
Chapter , Problem 12(choose chapter or problem)
Let{A1, A2, A3,...} be a sequence of events. Prove that if the series/ n=1 P (An) converges, then P * ) m=1 ( n=m An , = 0. This is called the Borel-Cantelli lemma. It says that if / n=1 P (An) < , the probability that infinitely many of the Ans occur is 0. Hint: Let Bm = ( n=m An and apply Theorem 1.8 to {Bm, m 1}.
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