Nath, Shambhu; Prasad, R. On convergence of probability measures in Banach space. (English) Zbl 1049.46008 Math. Educ. 36, No. 4, 237-240 (2002). Summary: Our main purpose here is to show that the boundedness of a Bernoulli sequence implies its convergence. It was derived by J. Kuelbs [Ann. Probab. 4, 744–771 (1976; Zbl 0365.60034)] that for a symmetric sequence of random variables, \(B(E)=C(E)\). We discuss here its impact in the context of Banach space. MSC: 46B09 Probabilistic methods in Banach space theory 60B11 Probability theory on linear topological spaces Keywords:Bernoulli sequences; boundedness; convergence Citations:Zbl 0365.60034 PDFBibTeX XMLCite \textit{S. Nath} and \textit{R. Prasad}, Math. Educ. 36, No. 4, 237--240 (2002; Zbl 1049.46008)