Ghosal, Subhashis; Chandra, Tapas K. Complete convergence of martingale arrays. (English) Zbl 0913.60029 J. Theor. Probab. 11, No. 3, 621-631 (1998). A sequence \(\{U_n, n\geq 1\}\) of random variables is said to converge completely to the constant \(c\) if \(\sum^\infty_{n= 1} P(| U_n- c|> \varepsilon)< \infty\) for all \(\varepsilon> 0\). The definition was introduced by P. L. Hsu and H. Robbins [Proc. Natl. Acad. Sci. USA 33, 25-31 (1947; Zbl 0030.20101)], and the authors also proved a result on complete convergence in the law of large numbers. The present paper is an extension to complete convergence for square-integrable martingale arrays together with several examples. Reviewer: A.Gut (Uppsala) Cited in 1 ReviewCited in 19 Documents MSC: 60F15 Strong limit theorems 60G42 Martingales with discrete parameter Keywords:complete convergence; law of large numbers; square-integrable martingale arrays Citations:Zbl 0030.20101 PDF BibTeX XML Cite \textit{S. Ghosal} and \textit{T. K. Chandra}, J. Theor. Probab. 11, No. 3, 621--631 (1998; Zbl 0913.60029) Full Text: DOI