On the definition of a probabilistic normed space |
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| Authors: | C. Alsina B. Schweizer A. Sklar |
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| Affiliation: | (1) Department of Mathematics and Statistics, Universitat Politècnica de Catalunya, E-08028 Barcelona, Spain;(2) Department of Mathematics and Statistics, University of Massachusetts, 01003 Amherst, Massachusetts, USA;(3) Department of Mathematics, Illinois Institute of Technology, 60616 Chicago, Illinois, USA |
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| Abstract: | Summary In this paper we give a new definition of a probabilistic normed space. This definition, which is based on a characterization of normed spaces by means of a betweenness relation, includes the earlier definition of A. N.  erstnev as a special case and leads naturally to the definition of the principal class of probabilistic normed spaces, the Menger spaces. |
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| Keywords: | Primary 46B99, 54E99 Secondary 60B11 |
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