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Borel–Cantelli Lemma for Capacities

Author

Listed:
  • Chunyu Kao

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Gaofeng Zong

    (School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China)

Abstract

In this paper, we investigate the second Borel–Cantelli lemma for capacity without the assumption of independence for events. We obtain a sufficient condition under which the second Borel–Cantelli lemma for capacity holds. Our results are natural extensions of the classical Borel–Cantelli lemma. However, the proof is different from the existing literature.

Suggested Citation

  • Chunyu Kao & Gaofeng Zong, 2025. "Borel–Cantelli Lemma for Capacities," Mathematics, MDPI, vol. 13(5), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:728-:d:1598314
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    References listed on IDEAS

    as
    1. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
    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. repec:dau:papers:123456789/7324 is not listed on IDEAS
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    5. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
    6. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    7. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
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