Title

Probabilistic Convergence Spaces

Authors

Authors

G. D. Richardson;D. C. Kent

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

probabilistic convergence space; initial probabilistic convergence; structure; probabilistic closure operator; Kowalsky diagonal axiom; Fischer diagonal axiom; Mathematics; Statistics & Probability

Abstract

A basic theory for probabilistic convergence spaces based on filter convergence is introduced. As in Florescu's previous theory of probabilistic convergence structures based on nets, one is able to assign a probability that a given filter converges to a given point. Various concepts and theorems pertaining to convergence spaces are extended to the realm of probabilistic convergence spaces, and illustrated by means of examples based on convergence in probability and convergence almost everywhere. Diagonal axioms due to Kowalsky and Fischer are also studied, first for convergence spaces and then in the setting of probabilistic convergence spaces.

Journal Title

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

Volume

61

Publication Date

1-1-1996

Document Type

Article

Language

English

First Page

400

Last Page

420

WOS Identifier

WOS:A1996VY88900010

ISSN

0263-6115

Share

COinS