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Ordered probabilistic metric spaces

Part of: Foundations of probability theory Generalities

Published online by Cambridge University Press:  09 April 2009

D. C. Kent  and
G. D. Richardson
D. C. Kent
Affiliation:
Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington 99164, U.S.A.
G. D. Richardson
Affiliation:
Departments of Mathematics and StatisticsUniversity of Central Florida, Orlando, Florida 32816, U.S.A.
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Abstract

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Probabilistic quasi-metric spaces are introduced and used to define ordered probabilistic metric spaces. The latter spaces arise naturally in the study of probability and statistics; they closely resemble the uniform ordered spaces of L. Nachbin. A procedure is described for constructing ordered probabilistic metric spaces from quasi-simple spaces, and a completions theory is developed simultaneously for probabilistic quasi-metric spaces and ordered probabilistic metric spaces.

Keywords

ordered probabilistic metic spaceuniform spaceCauchy filtercompletion.

MSC classification

Secondary: 54A05: Topological spaces and generalizations (closure spaces, etc.) 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 60A05: Axioms; other general questions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 88 - 99
Copyright
Copyright © Australian Mathematical Society 1989

References

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[3]Sherwood, H., ‘On the completion of probabilistic metric spaces’, Z. Wahrsch. Verw. Gebiete 6 (1966), 62–64.CrossRefGoogle Scholar
[4]Schweizer, B. and Sklar, A., Probabilistic metric spaces (North-Holland, New York, 1983).Google Scholar
[5]Schweizer, B. and Sklar, A., ‘Triangle inequalities in a class of statistical metric spaces’, J. London Math. Soc. 38 (1963), 401–406.CrossRefGoogle Scholar