• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.273-277
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• 1999

In this paper we will consider interval-valued martin-gales. We obtain several results parallel to the case of real-valued martingales. For example an $L_1$-bounded interval-valued martingale converges a.e. An interval-valued martingale ${{F_n}^\infty}_{n=1}$ is uniformly in-tegrable if and only if there is an interval-valued random variable F with $\parallel F \parallel _1<\infty$ such that $F_n=E(F\mid A_n)$, for all $n\geq 1$

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.827-840
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• 2009

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.