MA 222: Analysis II - Measure and Integration
Credits: 3:1
Prerequisite courses: MA 221
(Additional )Prerequisite courses for Undergraduates: UM 204
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 Radon-Nikodym theorem, Lp-spaces, Characterization of continuous linear functionals on Lp - spaces, Change of variables, Complex measures, Riesz representation theorem.
Suggested books and references:
- Royden, H. L., Real Analysis, Macmillan, 1988.
- Folland, G.B., Real Analysis: Modern Techniques and their Applications (2nd Ed.), Wiley.
- Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer, 1969.