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Zbl 0792.46062
Alsina, Claudi; Schweizer, Berthold; Sklar, Abe
On the definition of a probabilistic normed space. (English)
[J] Aequationes Math. 46, No.1-2, 91-98 (1993). ISSN 0001-9054; ISSN 1420-8903/e

It is given a new definition of a probabilistic normed space. Before the definition the authors somewhat change equivalently the axioms of a usual norm. The given definition includes the earlier definition of A. N. Serstnev as a special case and leads naturally to the definition of the principal class of probabilistic normed spaces, the Menger spaces.
[M.Ostrovskij (Khar'kov)]

MSC 2000:: *46S50 Functional analysis in probabilistic metric spaces
46B09 Probabilistic methods in Banach space theory
54E99 Topological spaces with richer structures
60B11 Probability theory on linear topological spaces

Keywords: probabilistic normed space; Menger spaces

Cited in: Zbl 1214.46058 Zbl 1214.46055 Zbl 1198.47075 Zbl 1179.46061 Zbl 1134.54007 Zbl 1142.54011 Zbl 1199.60210 Zbl 0945.46056 Zbl 0904.54025 Zbl 0903.46075 Zbl 0855.54042

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