Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

Use of this dissertation is restricted to the UNT Community. Off-campus users must log in to read.

Description

In this paper, exhaustivity, continuity, and strong additivity are studied in the setting of topological Riesz spaces. Of particular interest is the link between strong additivity and exhaustive elements of Dedekind s-complete Banach lattices. There is a strong connection between the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The Meyer-Nieberg Lemma is extended to the setting of topological Riesz spaces and uniform absolute continuity and uniformly exhaustive elements are studied in this setting. Counterexamples are provided to show that the Vitali-Hahn-Saks Theorem and the ... continued below

Creation Information

Muller, Kimberly O. May 2004.

Context

This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 73 times . More information about this dissertation can be viewed below.

Who

People and organizations associated with either the creation of this dissertation or its content.

Chair

Committee Members

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Muller, Kimberly O.

Provided By

UNT Libraries

With locations on the Denton campus of the University of North Texas and one in Dallas, UNT Libraries serves the school and the community by providing access to physical and online collections; The Portal to Texas History and UNT Digital Libraries; academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this dissertation. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

In this paper, exhaustivity, continuity, and strong additivity are studied in the setting of topological Riesz spaces. Of particular interest is the link between strong additivity and exhaustive elements of Dedekind s-complete Banach lattices. There is a strong connection between the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The Meyer-Nieberg Lemma is extended to the setting of topological Riesz spaces and uniform absolute continuity and uniformly exhaustive elements are studied in this setting. Counterexamples are provided to show that the Vitali-Hahn-Saks Theorem and the Brooks-Jewett Theorem cannot be extended to submeasures or to the setting of Banach lattices.

Subjects

Keywords

Library of Congress Subject Headings

Language

Identifier

Unique identifying numbers for this dissertation in the Digital Library or other systems.

Collections

This dissertation is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this dissertation?

When

Dates and time periods associated with this dissertation.

Creation Date

  • May 2004

Added to The UNT Digital Library

  • Feb. 15, 2008, 3:27 p.m.

Description Last Updated

  • Feb. 28, 2008, 10:07 a.m.

Usage Statistics

When was this dissertation last used?

Yesterday: 0
Past 30 days: 1
Total Uses: 73

Interact With This Dissertation

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Muller, Kimberly O. Exhaustivity, continuity, and strong additivity in topological Riesz spaces., dissertation, May 2004; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc4455/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .