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.
DOI
https://doi.org/10.57709/1895777
Recommended Citation
Kastine, Jeremiah D., "On the Lebesgue Integral." Thesis, Georgia State University, 2011.
doi: https://doi.org/10.57709/1895777