Bulletin of the
Korean Mathematical Society BKMS

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