This course will focus on measure theory and integration, covering the topics of Lebesgue measure and integral, abstract measure and integral, L2 and Lp spaces, elementary Hilbert space theory, absolute continuity, Radon-Nikodym theorem, product measure and integral.
Real Analysis'' by Folland
The classical theory of functions of a real variable: point-set topology, limits and continuity, differentiation and Riemann integration, infinite series, uniform convergence