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A generalization of the Borel-Cantelli lemma. (English) Zbl 1101.60300


MSC:

60A10 Probabilistic measure theory
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[1] Chung, K. L.; Erdös, P., On the application of the Borel-Cantelli lemma, Trans. Amer. Math. Soc., 72, 179-186 (1952) · Zbl 0046.35203
[2] Erdös, P.; Rényi, A., On Cantor’s series with convergent \(∑1/qn\), Ann. Univ. Sci. Budapest Sect. Math., 2, 93-109 (1959) · Zbl 0095.26501
[3] Kochen, S. P.; Stone, C. J., A note on the Borel-Cantelli lemma, Illinois J. Math., 8, 248-251 (1964) · Zbl 0139.35401
[4] Lamperti, J., Wiener’s tests and Markov chains, J. Math. Anal. Appl., 6, 58-66 (1963) · Zbl 0238.60044
[5] Martikainen, A. I.; Petrov, V. V., On the Borel-Cantelli lemma, Zapiski Nauch. Semin. Leningrad. Otd. Steklov Mat. Inst., 184, 200-207 (1990), (in Russian). English translation in: J. Math. Sci. 1994, 63, 540-544 · Zbl 0742.60019
[6] Ortega, J.; Wschebor, M., On the sequence of partial maxima of some random sequences, Stochastic Process. Appl., 16, 85-98 (1983) · Zbl 0523.60023
[7] Petrov, V. V., Limit Theorems of Probability Theory (1995), Oxford University Press: Oxford University Press Oxford · Zbl 0826.60001
[8] Petrov, V. V., A note on the Borel-Cantelli lemma, Statist. Probab. Lett., 58, 283-286 (2002) · Zbl 1017.60004
[9] Spitzer, F., Principles of Random Walk (1964), Van Nostrand: Van Nostrand Princeton · Zbl 0119.34304
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