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, Lp-spaces, Characterization of continuous linear functionals on Lp -
spaces, Change of variables, Complex measures, Riesz representation theorem.
- Royden, H. L., Real Analysis, Macmillan, 1988.
- Folland, G.B., Real Analysis: Modern Techniques and their Applications, 2nd
- Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer, 1969.
+91 (80) 2293 2711, +91 (80) 2293 2265 ; E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 01 Mar 2021