Geodesic
A generalization of the Chung-Erdös inequality for the probability of the union of events
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 147-150 
V. V. Petrov. A generalization of the Chung-Erdös inequality for the probability of the union of events. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 147-150. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a9/
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     title = {A generalization of the {Chung-Erd\"os} inequality for the probability of the union of events},
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     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A generalization of the Chung–Erdös inequality for the probability of the union of arbitrary events is proved using some lower bounds for tail probabilities. We present a lower bound for the probability of appearance of at least $m$ events from the set of events $A_1,\dots,A_n$ where $1\le m\le n$.

[1] K. L. Chung and P. Erdös, “On the application of the Borel–Cantelli lemma”, Trans. Amer. Math. Soc., 72 (1952), 179–186 | DOI | MR | Zbl

[2] V. V. Petrov, “On lower bounds for tail probabilities”, J. Statist. Planning and Inference, 137 (2007) | DOI | MR | Zbl

[3] B. C. Arnold, “Some elementary variations of the Lyapunov inequality”, SIAM J. Appl. Math., 35 (1978), 117–118 | DOI | MR | Zbl

[4] V. V. Petrov, “Odno neravenstvo dlya momentov sluchainoi velichiny”, Teoriya veroyatn. i ee primen., 20 (1975), 402–403 | MR | Zbl

[5] V. V. Petrov, Limit theorems of probability theory, Oxford University Press, New York, 1995 | MR | Zbl

[6] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 1, Mir, M., 1984