#### Title

#### Date of Award

Spring 1960

#### Degree Type

Thesis - Restricted

#### Degree Name

Master of Science (MS)

#### Department

Mathematics

#### First Advisor

Pettit, Harvey

#### Second Advisor

Heider, J. L.

#### Abstract

The concept of Lebesque integration has seemingly been reserved for students of advanced study. It is my aim to define and interpret the theory for the student of lesser advancement. I am assuming the reader has had an introductory course in the differential and integral calculus. The merit of the Riemannian integral is that it leads to numerical results. The functions in ordinary applications are bounded and continuous except possibly at a finite number of points, and hence are integrable in the sense of Riemann. For these functions the Lebesque integral equals the Riemann. However, the Lebesque integral is a generalization of the Riemann integral; it is applicable to bounded or unbounded functions and to infinite or finite ranges of integration. Consequently, the use of the integral calculus in applied or theoretical mathematics is readily translated to the Lebesque sense. Some knowledge of measure theory seems to be an advantage in this presentation. Hence, I have approached this treatise with some basic facts on the theory of measure and sets. After lengthly consideration of other developments, the following presentation seemed to me the best approach from an elementary standpoint.

#### Recommended Citation

Kennedy, Madeline L., "The Lebesgue Integral" (1960). *Master's Theses (1922-2009) Access restricted to Marquette Campus*. 2081.

https://epublications.marquette.edu/theses/2081