MA6110 TOPICS IN ADVANCED ANALYSIS
Review of general measure and integral; Positive Borel measures; Riesz representation theorem; Luzin's theorem; Vitali Caratheodory theorem. Lp-spaces and their dense subspaces,Complex measures; Absolute continuity; Radon-Nykodym theorem.Product measures; Fubini's theorem; Convolutions.
Derivatives of measures; Functions of bounded variation; Fourier transform.
W. Rudin: Real and Complex Analysis, Third edition, McGraw-Hill, International Editions, 1987.