Extensions of the Borel–Cantelli lemma in general measure spaces

Xuejun Wang, Xinghui Wang, Xiaoqin Li and Shuhe Hu ()
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Xuejun Wang: Anhui University
Xinghui Wang: Anhui University
Xiaoqin Li: Anhui University
Shuhe Hu: Anhui University

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1229-1248

Abstract: Abstract In this paper, an important bilateral inequality for a sequence of nonnegative measurable functions on a measure space $$(S,\mathcal {B}_S,\mu )$$ ( S , B S , μ ) is obtained, and some sufficient conditions for $$\mu \left( \limsup \limits _{n\rightarrow \infty }A_n\right) =\mu (S)$$ μ lim sup n → ∞ A n = μ ( S ) are given. In addition, a weighted version of the Borel–Cantelli Lemma on the measure space is obtained. Our results generalize the corresponding ones for bounded random sequences to the case of unbounded measurable functions.

Keywords: Borel–Cantelli lemma; Bilateral inequality; Measure space; 60E15; 60F20 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-013-0526-8

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