Real Analysis III

4 credits

Third 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. Prerequisites: MATH 240B. Students who have not completed MATH 240B may enroll with consent of instructor.