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On the convergence of certain sums of independent random elements

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J.C. Ferrando

On the convergence of certain sums of independent random elements

Comment.Math.Univ.Carolinae 43,1 (2002) 77-81.

Abstract: In this note we investigate the relationship between the convergence of the sequence {Sn} of sums of independent random elements of the form Sn = Pn

i=1εixi (whereεi takes the values±1 with the same probability and xi belongs to a real Banach space X for each i N) and the existence of certain weakly unconditionally Cauchy subseries ofP

n=1xn.

Keywords: independent random elements, copy of c0, Pettis integrable function, perfect measure space

AMS Subject Classification: 46B15, 46B09

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