Title

T-regular probabilistic convergence spaces

Authors

Authors

J. Minkler; G. Minkler;G. Richardson

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Aust. Math. Soc. A-Pure Math. Stat.

Keywords

convergence space; probabilistic convergence space; T-regular space; Mathematics; Statistics & Probability

Abstract

A probabilistic convergence structure assigns a probability that a given filter converges to a given element of the space. The role of the t-norm (triangle norm) in the study of regularity of probabilistic convergence spaces is investigated. Given a probabilistic convergence space, there exists a finest T-regular space which is coarser than the given space, and is referred to as the 'T-regular modification'. Moreover, for each probabilistic convergence space, there is a sequence of spaces, indexed by nonnegative ordinals, whose first term is the given space and whose last term is its T-regular modification. The T-regular modification is illustrated in the example involving 'convergence with probability lambda' for several t-norms. Suitable function space structures in terms of a given t-norm are also considered.

Journal Title

Journal of the Australian Mathematical Society Series a-Pure Mathematics and Statistics

Volume

64

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

210

Last Page

221

WOS Identifier

WOS:000073643300006

ISSN

0263-6115

Share

COinS