Complete convergence for arrays
Let \(\{(X_{nk}\), \(1\leq k\leq n)\), \(n\geq 1\}\) be an array of rowwise independent random variables. We extend and generalize some recent results due to \textit{T.-C. Hu}, \textit{F. Móricz} and \textit{R. L. Taylor} [Acta Math. Hung. 54, No. 1/2, 153-162 (1989; Zbl 0685.60032)] concerning complete convergence, in the sense of \textit{P. L. Hsu} and \textit{H. Robbins} [Proc. Natl. Acad. Sci. USA 33, 25-31 (1947; Zbl 0030.20101)], of the sequence of rowwise arithmetic means.
array of rowwise independent random variables
scientific article; zbMATH DE number 118338