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Comments on the paper: A bilateral inequality on the Borel-Cantelli Lemma

Author

Listed:
  • Hu, Shuhe
  • Wang, Xuejun
  • Li, Xiaoqin
  • Zhang, Yuanyuan

Abstract

A new extension of the Borel-Cantelli Lemma was obtained by Xie [Xie, Y.Q., 2008. A bilateral inequality on the Borel-Cantelli Lemma. Statist. Probab. Lett. 78, 2052-2057], and an important bilateral inequality on the Borel-Cantelli Lemma was given. However, there are several mistakes in the proof of Theorem 1 and Example 2 in the above cited reference. In this note we will present a corrected version of some results given therein.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:889-893
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    References listed on IDEAS

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    1. Chandra, Tapas Kumar, 2008. "The Borel-Cantelli lemma under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 390-395, March.
    2. Xie, Yuquan, 2008. "A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2052-2057, October.
    3. 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. Estrada, Luisa F. & Högele, Michael A., 2022. "Moment estimates in the first Borel–Cantelli Lemma with applications to mean deviation frequencies," Statistics & Probability Letters, Elsevier, vol. 190(C).
    2. Xie, Yuquan, 2009. "A bilateral inequality on a nonnegative bounded random sequence," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1577-1580, July.
    3. Ian Rowlands, 2011. "Ancillary impacts of energy-related climate change mitigation options in Africa’s least developed countries," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 16(7), pages 749-773, October.
    4. 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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