Tulane University 2006-2007 Catalog

Course:

MATH 671, 672 Analysis I and II (3, 3)

Staff. Prerequisites: MATH 305, 309, and 406. Lebesgue measure on R. Measurable functions (including Lusin's and Egoroff's theorems). The Lebesgue integral. Monotone and dominated convergence theorems. Radon-Nikodym Theorem. Differentiation: bounded variation, absolute continuity, and the fundamental theorem of calculus. Measure spaces and the general Lebesgue integral (including summation and topics in Rⁿ such as the Lebesgue differentiation theorem). L^p spaces and Banach spaces. Hahn-Banach, open mapping, and uniform boundedness theorems. Hilbert space. Representation of linear functionals. Completeness and compactness. Compact operators, integral equations, applications to differential equations, self-adjoint operators, unbounded operators.

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