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On Ito-Nisio type theorems for DS-groups. (English) Zbl 0890.60004
Author’s summary: It is shown that the convergence of convolution products of probability measures on certain non-locally compact topological Abelian groups can be verified by means of characteristic functionals. Analogous results are obtained also for almost everywhere convergence of series of independent random elements in the considered groups. A connection with the Sazonov property of the groups is discussed.
MSC:
60B10 Convergence of probability measures
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
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