1 Problem 7 11 Let A1, A2, be an infinite sequence of subsets with the property that k 1 P(Ak) Define the set C as C Ak for infinitely many k Use the continuity property of probabilities to prove that P(C) 0 (this result is known as the Borel Cantelli lemma)

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Question: 1. Problem 7.11 Let A1, A2,... be an infinite sequence of subsets with the property that k=1 P(Ak) < . Define the set C as

1. Problem 7.11 Let A1, A2,... be an infinite sequence of subsets with the property that k=1 P(Ak) < ∞. Define the set C as C ={ω: ω ∈ Ak for infinitely many k}. Use the continuity property of probabilities to prove that P(C) = 0 (this result is known as the Borel-Cantelli lemma).

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