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On the definition of a probabilistic normed space

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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. Šerstnev 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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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Universitat Politècnica de Catalunya, E-08028, Barcelona, Spain

    C. Alsina, B. Schweizer & A. Sklar

  2. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, Massachusetts, USA

    C. Alsina, B. Schweizer & A. Sklar

  3. Department of Mathematics, Illinois Institute of Technology, 60616, Chicago, Illinois, USA

    C. Alsina, B. Schweizer & A. Sklar

Authors
  1. C. Alsina
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  2. B. Schweizer
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  3. A. Sklar
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Alsina, C., Schweizer, B. & Sklar, A. On the definition of a probabilistic normed space. Aeq. Math. 46, 91–98 (1993). https://doi.org/10.1007/BF01834000

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  • DOI: https://doi.org/10.1007/BF01834000

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