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The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order ). In this paper, we give some new results of complete convergence in mean of order and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.
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