MA 301: Real Analysis

Credits: 3:0


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.

Suggested books and references:

  1. Royden, H. L., Real Analysis ,The Macmillan Company, New York, 1963.
  2. Rudin, W., Principles of Mathematical Analysis ,McGraw-Hill, 1986.
  3. Rudin, Functional Anaysis (2nd Ed.) ,McGraw-Hill, 2006.
  4. Hewitt, E. and Stromberg, K., Real and Abstract Analysis ,Springer International Student Edition, Springer-Verlag/Narosa Pub. House, New Delhi, 1978.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in