Date of Award

2011

Publication Type

Master Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Traynor, Tim (Mathematics & Statistics)

Keywords

Mathematics.

Rights

info:eu-repo/semantics/openAccess

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Abstract

In this paper we seek to investigate and compare several Kurzweil-Henstock type integrals. We present these integrals as special cases of a more general construction and establish key properties required in order to create similar "well behaved" integrals. After establishing basic results (additivity, monotonicity, etc.) for these integrals, we shift our focus to more interesting questions about them. We consider mainly the following topics: additivity, their relationship to the Lebesgue integral, absolute integrability, their relationships with each other, their relationship with differentiation, possible convergence theorems and the establishment of a Fubini Theorem.

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