J Austral Math Soc Ser A 46 pp88--99, 1989.

Ordered Probabilistic Metric Spaces

D. C. Kent and G. D. Richardson

Abstract

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 completion theory is developed simultaneously for probabilistic quasi-metric spaces and ordered probabilistic metric spaces.

1980 AMS Subject Classification (1985 Revision): 54A05, 43A20, 60A05

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Authors

D. C. Kent

Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington 99164, U.S.A.

G. D. Richardson

Department of Mathematics and Statistics, University of Central Florida, Orlando, Florida 32816, U.S.A.