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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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc4455
Date05 1900
CreatorsMuller, Kimberly O.
ContributorsLewis, Paul, Bator, Elizabeth M., Iaia, Joseph
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsUse restricted to UNT Community, Copyright, Muller, Kimberly O., Copyright is held by the author, unless otherwise noted. All rights reserved.

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