Mth 413 Introduction to Real Analysis III

Analysis on metric spaces, Baire Category, Contraction Mapping, and Stone-Weierstrass theorems. Lebesgue measure and integration theory, functions of bounded variation, absolutely continuous functions. Banach and Hilbert spaces. Bases and duality on Hilbert spaces, linear operators on Banach spaces. Introduction to Fourier series. This is the third course in a sequence of three: Mth 411, Mth 412 and Mth 413 which must be taken in sequence.