Date of Graduation

Summer 2009

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Xingping Sun

Keywords

Lebesgue, Riemann, convergence, integration, measure

Subject Categories

Mathematics

Abstract

In this paper, we examine the theory of integration of functions of real variables. Background information in measure theory and convergence is provided and several examples are considered. We compare Riemann and Lebesgue integration and develop several important theorems. In particular, the Monotone Convergence Theorem and Dominated Convergence Theorem are considered under both pointwise convergence and convergence in measure.

Copyright

© Ryan Vail Thomas

Open Access

Included in

Mathematics Commons

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