Geodesic
Complete convergence in mean for double arrays of random variables with values in Banach spaces
Applications of Mathematics, Tome 59 (2014) no. 2, pp. 177-190.

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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 $p$). In this paper, we give some new results of complete convergence in mean of order $p$ and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.
DOI : 10.1007/s10492-014-0048-4
Classification : 60B11, 60B12, 60F15, 60F25
Keywords: complete convergence in mean; double array of random variables with values in Banach space; martingale difference double array; strong law of large numbers; $p$-uniformly smooth space 
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     title = {Complete convergence in mean for double arrays of random variables with values in {Banach} spaces},
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Son, Ta Cong; Thang, Dang Hung; Dung, Le Van. Complete convergence in mean for double arrays of random variables with values in Banach spaces. Applications of Mathematics, Tome 59 (2014) no. 2, pp. 177-190. doi : 10.1007/s10492-014-0048-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0048-4/

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