# ON THE WEAK LAWS WITH RANDOM INDICES FOR PARTIAL SUMS FOR ARRAYS OF RANDOM ELEMENTS IN MARTINGALE TYPE p BANACH SPACES

• Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University) ;
• Hu, Tien-Chung (Department of Mathematics, National Tsing Hua University) ;
• Volodin, Andrei I. (Department of Mathematics and Statistics, University of Regina)
• Published : 2006.08.01
• 85 3

#### Abstract

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large 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 쇼;e p Banach space;weak law of large numbers;randomly indexed sums;martingale difference sequence;Cesaro type condition

#### References

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