Date of Award
8-1966
Document Type
Thesis
Degree Name
Master of Science
Degree Discipline
Mathematics
Abstract
The primary objective of this paper is a close examination of the differences in the class of functions f and g when f is Integrable with respect to g according to the definition of the integral based on the use of upper and lower sums as compared to the definition of the integral based on the trapezodial sum approach. The differences in the proofs of certain theorems relative to the properties and existence of the Integral will also be examined.
In order to clearly distinguish between these approaches to the integral, the writer considers only one method of taking limits of the defining sums, namely the refining of partitions. Clearly, the limit of these sums under the requirement of the norm of the partitioning having limit zero introduces another difference in the possible existence of the integral and is not considered in this paper.
Committee Chair/Advisor
Ralph Whitmore
Committee Member
A. D. Stewart
Publisher
Prairie View Agricultural and Mechanical College
Rights
© 2021 Prairie View A & M University
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Date of Digitization
10/20/2021
Contributing Institution
John B Coleman Library
City of Publication
Prairie View
MIME Type
Application/PDF
Recommended Citation
Arceneaux, L. (1966). A Comparative Study Of Two Methods Of Defining The Stieltjes Integrals. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/564