REAL ANALYSIS
The Lebesgue Integral:Riemann-Stieltjes integral, Measures and measurable sets, measurable functions, the abstract Lebesgue integral. Product measures and Fubini’s theorem. Complex measures and the lebesgue - Radon - Nikodym theorem and its applications. Function Spaces and Banach Spaces: Lpspaces, Abstract Banach Spaces. The conjugate spaces. Abstract Hilbert spaces.
Books
- Royden, H. L., Real Analysis, The Macmillan Company, New York, 1963.
- Rudin, W., Real and Complex Analysis, Second Edition, Tata McGraw Hill Publishing Co. Ltd., New Delhi, 1974.
- Rudin, W., Functional Analysis, Tata McGraw Hill Publishing Co. Ltd., New Delhi, 1973.
- Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer International Student Edition, Springer-Verlag/Narosa Pub. House, New Delhi, 1978.