Title

Convergence In Probabilistic Semimetric Spaces

Comments

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Abbreviated Journal Title

J. Risk Insur.

Keywords

Mathematics

Abstract

Let (S, F) denote a probabilistic semimetric space. An induced Cauchy structure on S is shown to be a natural means of studying convergence and completion theory. A convergent sequence is also required to be Cauchy. This is a fundamental difference between our convergence notion and that studied previously. However, if (S, F, τ) is a probabilistic metric space with τ continuous, then the definitions coincide because of the triangle inequality. Moreover, the requirement that F be Cauchy-continuous, along with the restriction that a convergent sequence be Cauchy, helps to capture the geometry of the triangle inequality. It is shown that every probabilistic semimetric space (S, F) is the image of a simple space under a Cauchy-quotient map whenever F is Cauchy-continuous. Sufficient conditions are given to ensure that a probabilistic semimetric space has a completion (compactification).

Journal Title

Journal of Risk and Insurance

Volume

18

Issue/Number

3

Publication Date

1-1-1988

Document Type

Article

Language

English

First Page

617

Last Page

634

WOS Identifier

WOS:A1988R580500008

ISSN

0035-7596

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