Real Analysis II

Catalog description

Description: Differentiation with respect to measures. Aspects of point set topology: nets, locally compact spaces, product spaces. Elementary functional analysis: Hahn-Banach, uniform boundedness, open mapping theorems, weak topologies, Hilbert spaces. Riesz representation theorems: duals of Lebesgue spaces and spaces of continuous functions. Other topics may include: elements of Fourier analysis, distribution theory, Stone-Weierstrass theorem.