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

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2004

Author dc:creator

• Muller, Kimberly O.

Contributors dc:contributor

• Lewis, Paul
• Bator, Elizabeth M.
• Iaia, Joseph

• Riesz spaces.
• exhaustivity
• continuity
• strong additivity
• exhaustive elements
• topological Reisz space

Statement dc:rights

• Use restricted to UNT Community
• Copyright
• Muller, Kimberly O.
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 55941031
https://digital.library.unt.edu/ark:/67531/metadc4455/
ark: ark:/67531/metadc4455

OAI identifier oai:identifier

info:ark/67531/metadc4455