Bull. Korean Math. Soc. 2006; 43(3): 543-549
Printed September 1, 2006
Copyright © The Korean Mathematical Society.
Soo Hak Sung, Tien-Chung Hu, and Andrei I. Volodin
Pai Chai University, National Tsing Hua University, University of Regina
Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{ X_{ni}, u_n \le i \le v_n , n\ge 1\}$ of random variables under a Ces\`aro type condition, where $\{u_n\ge -\infty, n\ge 1\}$ and $\{v_n\le +\infty, n\ge 1\}$ are two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type $p$ Banach space.
Keywords: arrays of random elements, convergence in probability, martingale type $p$ Banach space, weak law of large numbers, randomly indexed sums, martingale difference sequence, Cesaro type condition
MSC numbers: 60B11, 60B12, 60F05, 60G42
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