Date of Award

Spring 3-18-2011

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Imre Patyi

Second Advisor

Dr. Changyong Zhong

Third Advisor

Dr. Alexandra Smirnova

Abstract

We look from a new point of view at the definition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Hausdorff spaces. We use mini sums to give all of them a unified treatment that is more efficient than the standard ones. We also give Fubini's theorem a proof that is nicer and uses much lighter technical baggage than the usual treatments.

Included in

Mathematics Commons

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