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A note on the Borel-Cantelli lemma. (English) Zbl 1017.60004

From the author’s abstract: A generalization of the Erdős-Rényi formulation of the Borel-Cantelli lemma is obtained.

MSC:

60A05 Axioms; other general questions in probability
60A10 Probabilistic measure theory
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References:

[1] Chung, K. L.; Erdös, P., On the application of the Borel-Canlelli 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. B.; 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 test and Markov chains, J. Math. Anal. Appl., 6, 58-66 (1963) · Zbl 0238.60044
[5] Martikainen, A.I., Petrov, V.V., 1990. On the Borel-Cantelli lemma. Zapiski Nauchn Sem. Leningrad. Otdel Mat. Inst. Steklov. 184, 200-207 (in Russian) (English transl. in: J. Math. Sci. , 1994, 63, 540-544).; Martikainen, A.I., Petrov, V.V., 1990. On the Borel-Cantelli lemma. Zapiski Nauchn Sem. Leningrad. Otdel Mat. Inst. Steklov. 184, 200-207 (in Russian) (English transl. in: J. Math. Sci. , 1994, 63, 540-544). · Zbl 0742.60019
[6] Petrov, V. V., Limit Theorems of Probability Theory (1995), Oxford University Press: Oxford University Press Oxford · Zbl 0826.60001
[7] Spitzer, F., Principles of Random Walk (1964), Van Nostrand: Van Nostrand Princeton · Zbl 0119.34304
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