M.Sc-I Sem-I 

course Na

MT - 501: Real Analysis
1.  Measure   Theory:   Preliminaries,   Exterior   Measure,   Measurable   Sets   and Lebesgue Measure, Measurable Functions.
2.  Integration Theory: The Lebesgue Integral, basic properties and convergence theorems. The space L^1 of integrable functions, Fubini’s theorem.
3.  Differentiation and Integration: Differentiation of the integral, Good kernels and approximation to the identity, differentiation of functions.
Text Book: Real Analysis, E. Stein and R. Shakharchi, New Age International Publishers, Princeton Lecture Notes III. Chapter 1 - Sections 1 to 4,  Chapter  2  - Sections 1 to 3, Chapter 3 - Sections 1 to 3.
Reference Books:
1. Karen Saxe : Beginning Functional Analysis (Springer International Edition)
2. N. L. Carothers: Real Analysis (Cambridge University Press)
3. W. Rudin : Principles of Mathematical Analysis (Mc-Graw Hill)
4. H. Royden, Real Analysis, McMillan Publishing Company