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On convergence of probability measures in Banach space. (English) Zbl 1049.46008

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

Citations:

Zbl 0365.60034
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