Buldygin, V. V.; Solntsev, S. A. On weak and strong almost sure convergence of series of independent random elements in Banach spaces. (English. Russian original) Zbl 0926.60023 Theory Probab. Math. Stat. 56, 61-66 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 61-66 (1997). Conditions of equivalence of the almost sure convergence in norm and sufficiently weak almost sure convergence for series of independent random elements in a separable Banach space are stated. Some examples are considered to demonstrate the exactness of these conditions. Reviewer: A.V.Swishchuk (Kyïv) MSC: 60F05 Central limit and other weak theorems 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 60F15 Strong limit theorems Keywords:strong and weak convergence; series of independent random elements in Banach space PDFBibTeX XMLCite \textit{V. V. Buldygin} and \textit{S. A. Solntsev}, Teor. Ĭmovirn. Mat. Stat. 56, 61--66 (1997; Zbl 0926.60023); translation from Teor. Jmovirn. Mat. Stat. 56, 61--66 (1997)