Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1989 - Volume 46, Issue 01  

Research Article

Ordered probabilistic metric spaces

D. C. Kenta1 and G. D. Richardsona2

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.

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 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)

  • 54 A 05;
  • 54 A 20;
  • 60 A 05

Keywords and phrases

  • ordered probabilistic metic space;
  • uniform space;
  • Cauchy filter;
  • completion.