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J. Korean Math. Soc. 2007; 44(2): 467-476
Printed March 1, 2007
Copyright © The Korean Mathematical Society.
On complete convergence for arrays of rowwise independent random elements
Soo Hak Sung, Manuel Ordonez Cabrera, and Tien-Chung Hu
Pai Chai University, University of Sevilla, Tsing Hua University
A complete convergence theorem for arrays of rowwise independent random variables was proved by Sung, Volodin, and Hu [14]. In this paper, we extend this theorem to the Banach space without any geometric assumptions on the underlying Banach space. Our theorem also improves some known results from the literature.
Keywords: Banach space valued random elements, complete convergence, rowwise independence, sums of independent random elements, convergence in probability
MSC numbers: 60B12, 60F15, 60F05
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