**ANALYSIS II: MEASURE AND INTEGRATION **

Construction of Lebesgue measure, Measurable functions, Lebesgue integration, Abstract measure and abstract integration, Monotone convergence theorem, Dominated convergence theorem, Fatou's lemma, Comparison of Riemann integration and Lebesgue integration, Product sigma algebras, Product measures, Sections of measurable functions, Fubini's theorem, Signed measures and Randon-Nikodym theorem, L^{p}-spaces, Characterization of continuous linear
functionals on L^{p} -spaces, Change of variables, Complex measures, Riesz representation theorem.

**Recommended books**

- Royden, H. L., Real Analysis, Macmillan, 1988.
- Folland, G.B., Real Analysis: Modern Techniques and their Applications, 2nd edition, Wiley.
- Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer, 1969.