Date of Award
Master of Science
Master of Mathematics
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.
A. D. Stewart
Prairie View Agricultural and Mechanical College
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Date of Digitization
John B Coleman Library
City of Publication
Arceneaux, L. (1966). A Comparative Study Of Two Methods Of Defining The Stieltjes Integrals. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/564