Borel–Cantelli Lemma for Capacities

Chunyu Kao () and Gaofeng Zong
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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

Mathematics, 2025, vol. 13, issue 5, 1-10

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.

Keywords: capacity; Choquet expectation; exponential independence; law of large numbers; sub-linear expectation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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