Complete convergence theorems for weighted row sums from arrays of random elements in Rademacher type p and martingale type p Banach spaces

Abstract

In this correspondence, complete convergence theorems are established for weighted row sums from arrays of random elements taking values in real separable Rademacher type Banach spaces as well as real separable martingale type Banach spaces. It is assumed that A version of the Rademacher type p complete convergence theorem is also established with random variable weights. Illustrative examples are included.