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Zbl 0903.46075
Alsina, Claudi; Schweizer, Berthold; Sklar, Abe
Continuity properties of probabilistic norms. (English)
[J] J. Math. Anal. Appl. 208, No.2, 446-452 (1997). ISSN 0022-247X

A. N. Serstnev introduced the notion of probabilistic spaces which was recently modified by {\it C. Alsina}, {\it B. Schweizer} and {\it 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.
[Ismat Beg (Kuwait)]

MSC 2000:: *46S50 Functional analysis in probabilistic metric spaces
46B09 Probabilistic methods in Banach space theory
54E70 Probabilistic metric spaces
60B11 Probability theory on linear topological spaces

Keywords: continuity; probabilistic normed spaces

Citations: Zbl 0792.46062

Cited in: Zbl 1143.54012

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