Publication Date

Fall 2017

Document Type


Degree Name

Master of Science



First Advisor

Andrius Tamulis, Ph.D.

Second Advisor

Dianna Galante, Ph.D.

Third Advisor

J. Christopher Tweddle, Ph.D.


The Riemann integral is the simplest integral to define, and it allows one to integrate every continuous function. It is really important to have a definition of the integral that allows a wider class of functions to be integrated. However, there are many other types of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue integral requires the use of measure theory since picking out a suitable class of measurable subsets is an essential prerequisite for Lebesgue integral. The central concepts in this paper are Lebesgue measure and the Lebesgue integral. Examples as well as theorems and proofs will be presented in this paper. In addition, this paper will present some details about the Fundamental Theorem of Calculus for Lebesgue integral.