Date of Graduation
Master of Science in Mathematics
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.
Lebesgue, Riemann, convergence, integration, measure
© Ryan Vail Thomas
Thomas, Ryan Vail, "Convergence and the Lebesgue Integral" (2009). MSU Graduate Theses. 1631.