MATH 240BReal Analysis II
Second course in graduate real analysis. Abstract measure and integration theory, integration on product spaces. Lebesgue measure and integral, Lebesgue-Stieltjes integrals, functions of bounded variation, differentiation of measures. Locally compact Hausdorff spaces, Banach and Hilbert spaces, linear functionals. Lebesgue spaces and interpolation, elements of Fourier analysis and distribution theory.