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University of North Texas

1. Muller, Kimberly O. Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

Degree: 2004, University of North Texas

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. Advisors/Committee Members: Lewis, Paul, Bator, Elizabeth M., Iaia, Joseph.

Subjects/Keywords: Riesz spaces.; exhaustivity; strong additivity; topological Reisz space

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Muller, K. O. (2004). Exhaustivity, continuity, and strong additivity in topological Riesz spaces. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc4455/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Muller, Kimberly O. “Exhaustivity, continuity, and strong additivity in topological Riesz spaces.” 2004. Thesis, University of North Texas. Accessed August 23, 2019. https://digital.library.unt.edu/ark:/67531/metadc4455/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Muller, Kimberly O. “Exhaustivity, continuity, and strong additivity in topological Riesz spaces.” 2004. Web. 23 Aug 2019.

Vancouver:

Muller KO. Exhaustivity, continuity, and strong additivity in topological Riesz spaces. [Internet] [Thesis]. University of North Texas; 2004. [cited 2019 Aug 23]. Available from: https://digital.library.unt.edu/ark:/67531/metadc4455/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Muller KO. Exhaustivity, continuity, and strong additivity in topological Riesz spaces. [Thesis]. University of North Texas; 2004. Available from: https://digital.library.unt.edu/ark:/67531/metadc4455/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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