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Zbl 1121.54050
Sempi, Carlo
A short and partial history of probabilistic normed spaces. (English)
[J] Mediterr. J. Math. 3, No. 2, 283-300 (2006). ISSN 1660-5446; ISSN 1660-5454/e

In this paper Carlo Sempi makes an interesting survey on the theory of probabilistic normed spaces. The survey describes clearly which has been the evolution of this theory in the framework of probabilistic metric spaces with special attention to the original definition (1962) of A. N. Sherstnev and to the new approach (1993) of C. Alsina, B. Schweizer and A. Sklar. Then a detailed overview of all contributions made to the theory is given. This complete description gives to the present paper a great interest for those interested in the theory. Moreover key open problems are stated.
[Claudi Alsina (Barcelona)]

MSC 2000:: *54E70 Probabilistic metric spaces
46S50 Functional analysis in probabilistic metric spaces
54-03 Historical (general topology)
46-03 Historical (functional analysis)

Keywords: Probabilistic normed space; probabilistic metric space; probabilistic norm; triangle function

Cited in: Zbl 1179.54047

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