Measure Theory
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, Lp-spaces, Characterization of continuous linear functionals on Lp - spaces, Change of variables, Complex measures, Riesz representation theorem. Recommended books
- Rudin, W., Real and Complex Analysis, McGraw-Hill, 1986.
- Royden, H. L., Real Analysis, Macmillan, 1988.
- Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer, 1969.
- De Barra, G., Introduction to Measure Theory, Von Nostrand Reinhold, 1974.