Date of Award
2006
Document Type
Thesis
Degree Name
Master of Arts in Mathematics
Department
Mathematics
First Advisor
Ventura, Belisario
Second Advisor
Hasan, Zahid
Third Advisor
Trapp, Rolland
Abstract
The thesis studies the notions of outer measure, Lebesgue measurable sets and Lebesgue measure, in detail. After developing Lebesgue integration over the real line, the Riemann integrable functions are classified as those functions whose set of points of discontinuity has measure zero. The convergence theorems are proven and it is shown how these theorems are valid under less stringent assumptions that are required for the Riemann integral. A detailed analysis of abstract measure theory for general measure spaces is given.
Recommended Citation
McLoughlin, Sara Hernandez, "From measure to integration" (2006). Theses Digitization Project. 4311.
https://scholarworks.lib.csusb.edu/etd-project/4311
