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MATH 55003. Theory of Functions of a Real Variable I. 3 Hours.

Real number system, Lebesque measure, Lebesque integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus L^P spaces, Holder and Minkowski inequalities, and bounded linear functionals on the L^P spaces. Prerequisite: ²Ñ´¡°Õ±áÌý45203 or ²Ñ´¡°Õ±áÌý52203, and graduate standing in mathematics or statistics, or departmental consent. (Typically offered: Fall)