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A bilateral inequality on the Borel-Cantelli Lemma

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  • Xie, Yuquan

Abstract

Let A1,A2,... be a sequence of events satisfying the condition , IAi be the indicator function for the event Ai, , Tn=SnI(Sn>0)/ESn; we have an important bilateral inequality as follows: and several of the well-known results on the generalizations of the Borel-Cantelli Lemma are special cases of this result.

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  • Xie, Yuquan, 2008. "A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2052-2057, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2052-2057
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    References listed on IDEAS

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    1. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
    2. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
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    Cited by:

    1. Xie, Yuquan, 2009. "A bilateral inequality on a nonnegative bounded random sequence," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1577-1580, July.
    2. Hu, Shuhe & Wang, Xuejun & Li, Xiaoqin & Zhang, Yuanyuan, 2009. "Comments on the paper: A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 889-893, April.
    3. Liu, Jicheng, 2012. "A note on the bilateral inequality for a sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 871-875.

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