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Convergence And The Lebesgue Integral, Ryan Vail Thomas
Convergence And The Lebesgue Integral, Ryan Vail Thomas
MSU Graduate Theses
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.