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University of North Texas

1. Huff, Cheryl Rae. Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices.

Degree: 1999, University of North Texas

The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical continuous function spaces C(K). Numerous authors have worked extensively on extending and generalizing the theorems of the preceding authors. Specifically, we mention Bilyeu and Lewis as well as Brooks and Drewnowski, whose efforts molded the direction and focus of this paper. This paper is a study of the techniques used by Bell, Bilyeu, and Lewis in their paper on uniform exhaustivity and Banach lattices to present a Banach lattice version of two important and powerful results in measure theory by Brooks and Drewnowski. In showing that the notions of exhaustivity and continuity take on familiar forms in certain Banach lattices of measures they show that these important measure theory results follow as corollaries of the generalized Banach lattice versions. This work uses their template to generalize results established by Bator, Bilyeu, and Lewis. Advisors/Committee Members: Lewis, Paul Weldon, Bator, Elizabeth M., Jackson, Steve, 1957-.

Subjects/Keywords: uniform exhaustivity; Banach lattices; mathematics; Banach lattices.; Measure theory.

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

APA (6th Edition):

Huff, C. R. (1999). Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc278330/

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):

Huff, Cheryl Rae. “Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices.” 1999. Thesis, University of North Texas. Accessed September 18, 2020. https://digital.library.unt.edu/ark:/67531/metadc278330/.

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

MLA Handbook (7th Edition):

Huff, Cheryl Rae. “Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices.” 1999. Web. 18 Sep 2020.

Vancouver:

Huff CR. Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices. [Internet] [Thesis]. University of North Texas; 1999. [cited 2020 Sep 18]. Available from: https://digital.library.unt.edu/ark:/67531/metadc278330/.

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

Council of Science Editors:

Huff CR. Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices. [Thesis]. University of North Texas; 1999. Available from: https://digital.library.unt.edu/ark:/67531/metadc278330/

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

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