• Honam Mathematical Journal
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• v.36 no.4
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• pp.767-775
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• 2014

In this paper we define the extended conditional negative quadrant dependence and generalize the conditional Borel-Cantelli lemma of B.L.S. Prakasa Rao(2012) to the case of pairwise extended conditionally negative quadrant dependence.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.441-460
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• 2017

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.