a1 Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington 99164, U.S.A.
a2 Departments of Mathematics and Statistics University of Central Florida, Orlando, Florida 32816, U.S.A.
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.
(Received August 01 1986)
(Revised March 05 1987)
1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)
Keywords and phrases