Ferrando, J. C. On the convergence of certain sums of independent random elements. (English) Zbl 1090.46009 Commentat. Math. Univ. Carol. 43, No. 1, 77-81 (2002). Summary: In this note, we investigate the relationship between the convergence of the sequence \(\{S_{n}\}\) of sums of independent random elements of the form \(S_{n}=\sum _{i=1}^{n}\varepsilon _{i}x_{i}\) (where \(\varepsilon _{i}\) takes the values \(\pm 1\) with the same probability and \(x_{i}\) belongs to a real Banach space \(X\) for each \(i\in \mathbb N\)) and the existence of certain weakly unconditionally Cauchy subseries of \(\sum _{n=1}^{\infty }x_{n}\). MSC: 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces 46B09 Probabilistic methods in Banach space theory Keywords:independent random elements; copy of \(c_{0}\); Pettis integrable function; perfect measure space PDF BibTeX XML Cite \textit{J. C. Ferrando}, Commentat. Math. Univ. Carol. 43, No. 1, 77--81 (2002; Zbl 1090.46009) Full Text: EuDML EMIS OpenURL