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On the Borel-Cantelli lemma. (Russian) Zbl 0742.60019

Let \(\{A_ n\}\) be an infinite sequence of events in a given probability space. Estimations are derived for \(P(A_ n\) infinitely often), and necessary and sufficient conditions are presented for this probability to be equal to \(\alpha\) \((0\leq\alpha\leq 1)\).
English translation in J. Math. Sci., New York 68, No. 4, 540–544 (1990; Zbl 0836.60013).

MSC:

60E15 Inequalities; stochastic orderings
60F20 Zero-one laws

Citations:

Zbl 0836.60013
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