On the weak laws with random indices for partial sums for arrays of random elements in martingale type $p$ Banach spaces

摘要

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array ${ X_{ni}, u_n le i le v_n , nge 1}$ of random variables under a Ces`aro type condition, where ${u_nge -infty, nge 1}$ and ${v_nle +infty, nge 1}$ are two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type $p$ Banach space.