A Complete Convergence Theorem for Row Sums from Arrays of Rowwise Independent Random Elements in Rademacher Type p Banach Spaces

We extend in several directions a complete convergence theorem for row sums from an array of rowwise independent random variables obtained by Sung, Volodin, and Hu [8 Sung , S.H. , Volodin , A.I. , and Hu , T.-C. ( 2005 ). More on complete convergence for arrays. Statist. Probab. Lett. 71:303–311.  [Google Scholar]] to an array of rowwise independent random elements taking values in a real separable Rademacher type p Banach space. An example is presented which illustrates that our result extends the Sung, Volodin, and Hu result even for the random variable case.