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Continuity properties of probabilistic norms. (English) Zbl 0903.46075
A. N. Serstnev introduced the notion of probabilistic spaces which was recently modified by C. Alsina, B. Schweizer and A. Sklar [Aequationes Math. 46, No. 1-2, 91-98 (1993; Zbl 0792.46062)]. In this interesting paper, the authors investigate questions of continuity in probabilistic normed spaces. It is proved that vector addition is continuous with respect to the norm-induced topology where as multiplication by a fixed scalar can be discontinuous.
Reviewer: Ismat Beg (Kuwait)

46S50 Functional analysis in probabilistic metric linear spaces
46B09 Probabilistic methods in Banach space theory
54E70 Probabilistic metric spaces
60B11 Probability theory on linear topological spaces
Full Text: DOI
[1] Alsina, C.; Schweizer, B.; Sklar, A., On the definition of a probabilistic normed space, Aequationes math., 46, 91-98, (1993) · Zbl 0792.46062
[2] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), Elsevier/North-Holland New York · Zbl 0546.60010
[3] ҆erstnev, A.N., On the notion of a random normed space, Dokl. akad. nauk SSSR, 149, 280-283, (1963)
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