Geodesic
On the Borel-Cantelli Problem
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 273-275

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Let (Ω, , P) be a probability space, and A 1, A 2... be a sequence of members of . The classical Borel-Cantelli problem is to determine the probability that infinitely many events A k occur. The classical results may be found in Feller [2, p. 188]; while related work may be found in Spitzer [3, p. 317], and Dawson and Sankoff [1]. The latter works are generalizations of the Borel-Cantelli lemmas, taken in different directions.In this paper, necessary and sufficient conditions will be given for infinitely many events A k to occur, with probability 1. A lower bound for the probability that only finitely many A k occur, is developed. In addition, necessary and sufficient conditions that only finitely many A k occur, with probability 1, are given. 
Shuster, Jonathan. On the Borel-Cantelli Problem. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 273-275. doi: 10.4153/CMB-1970-054-2
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     title = {On the {Borel-Cantelli} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {273--275},
     year = {1970},
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     number = {2},
     doi = {10.4153/CMB-1970-054-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-054-2/}
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