MATH 601 - Measure Theory

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Measure and integration: sigma-algebras, measures, outer measures, Borel measures on R, measurable functions, integration of non-negative functions, mode of convergence, product measures, Lebesgue integral on R, decomposition and differentiation of measures, signed measures, the Lebesgue- Radon-Nikodym theorem, differentiation on R, functions of bounded variation spaces, basic theory of Lp spaces and the dual of Lp.
Prerequisite: Prerequisite: MATH 302, MATH 401 or consent of instructor.