Integrated MSc-PhD Program

SYLLABUS

KSM2C02: Analysis II

The problem of measure, Lebesgue measure, The Lebesgue integral, Abstract measure spaces, Modes of convergence, Differentiation theorems, Outer measures, pre-measures, and product measures Measure spaces, Fubini, Radon-Nikodym derivative.

Suggested texts:

1. 1. 1. 1. 1. 1. Terence Tao, An introduction to Measure Theory, AMS publication.
               2. Gerald B. Folland, Real analysis, second ed., Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1999, Modern techniques and their applications, A Wiley-Interscience Publication.
               3. Elias M. Stein and Rami Shakarchi, Real analysis, Princeton Lectures in Analysis, vol. 3, Princeton University Press, Princeton, NJ, 2005, Measure theory, integration, and Hilbert spaces.
               4. Walter Rudin, Real and complex analysis, third ed., McGraw-Hill Book Co., New York, 1987.