Abstract
dc:description.abstract<p>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.</p>
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- Thesis
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2017
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Adi, Ikhlas
- Contributors dc:contributor
-
- Andrius Tamulis, Ph.D.
- Dianna Galante, Ph.D.
- J. Christopher Tweddle, Ph.D.
Subjects
dc:subject × 2Identifiers
dc:identifier.*- Repository record dc:identifier
- https://opus.govst.edu/theses/108
- OAI identifier oai:identifier
- oai:opus.govst.edu:theses-1110