MATH 6121 - Real Variables I

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P: MATH 5101 or consent of instructor I. Study of functions of one real variable and convergence of sequences and series of functions: functions of bounded variation, measures, measurable sets, measurable functions, convergence almost everywhere, absolutely continuous functions, Lebesque integration, differentiation, and the Fundamental Theorem of the Calculus. II. Lebesque spaces and associated inequalities, measures in Rn, measure spaces and the associated theory of integration and differentiation; the Radon-Nikodym Theorem with applications to probability and statistics.