Mth 412 Introduction to Real Analysis II

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 second course in a sequence of three: Mth 411, Mth 412 and Mth 413 which must be taken in sequence.