Anna Kuczmaszewska, Dominik Szynal, "On complete convergence in a Banach space", International Journal of Mathematics and Mathematical Sciences, vol. 17, Article ID 948642, 14 pages, 1994. https://doi.org/10.1155/S0161171294000013
On complete convergence in a Banach space
Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.
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