{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc4455"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc4455","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"Exhaustivity, continuity, and strong additivity in topological Riesz spaces.","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Muller, Kimberly O."],"institution":"University of North Texas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Lewis, Paul","Bator, Elizabeth M.","Iaia, Joseph"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-05","date_published":"2004-05","updated_at":"2026-07-24T05:35:09Z","subjects":["Riesz spaces.","exhaustivity","continuity","strong additivity","exhaustive elements","topological Reisz space"],"languages":["English"],"rights":["Use restricted to UNT Community","Copyright","Muller, Kimberly O.","Copyright is held by the author, unless otherwise noted. All rights reserved."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oclc: 55941031","https://digital.library.unt.edu/ark:/67531/metadc4455/","ark: ark:/67531/metadc4455"],"render_values":[{"text":"oclc: 55941031","href":null,"code":true},{"text":"https://digital.library.unt.edu/ark:/67531/metadc4455/","href":"https://digital.library.unt.edu/ark:/67531/metadc4455/","code":true},{"text":"ark: ark:/67531/metadc4455","href":null,"code":true}]}]},"links":{"outbound_url":"https://doi.org/10.12794/metadc4455","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lewis, Paul","Bator, Elizabeth M.","Iaia, Joseph"]},{"key":"dc:creator","label":"Author","values":["Muller, Kimberly O."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2004-05"]},{"key":"dc:publisher","label":"Institution","values":["University of North Texas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Riesz spaces.","exhaustivity","continuity","strong additivity","exhaustive elements","topological Reisz space"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["Use restricted to UNT Community","Copyright","Muller, Kimberly O.","Copyright is held by the author, unless otherwise noted. 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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."]},{"key":"dc:format","label":"Dc Format","values":["Text"]},{"key":"dc:title","label":"Title","values":["Exhaustivity, continuity, and strong additivity in topological Riesz spaces."]}]}],"canonical_facts":{"dc:contributor":["Lewis, Paul","Bator, Elizabeth M.","Iaia, Joseph"],"dc:creator":["Muller, Kimberly O."],"dc:date":["2004-05"],"dc: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."],"dc:format":["Text"],"dc:identifier":["oclc: 55941031","doi: 10.12794/metadc4455","https://digital.library.unt.edu/ark:/67531/metadc4455/","ark: ark:/67531/metadc4455"],"dc:language":["English"],"dc:publisher":["University of North Texas"],"dc:rights":["Use restricted to UNT Community","Copyright","Muller, Kimberly O.","Copyright is held by the author, unless otherwise noted. All rights reserved."],"dc:subject":["Riesz spaces.","exhaustivity","continuity","strong additivity","exhaustive elements","topological Reisz space"],"dc:title":["Exhaustivity, continuity, and strong additivity in topological Riesz spaces."],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:35:09Z"}