USC Schedule of Classes

a: Measure and integration over abstract measure spaces, Radon-Nikodym theorem, Fubini's theorem, convergence theorems, differentiation. Prerequisite: 425ab. b: Metric spaces, contraction principle, category, Banach spaces, Riesz representation theorem, properties of Lp, Hilbert spaces, orthogonal expansions, Fourier series and transforms, convolutions. Prerequisite: 525a.