**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Lebesgue integral and construction of Lebesgue measure on , Non measurable sets, Fatou's Lemma and Convergence Theorems, spaces and their completeness, Reisz representation Theorem for ; locally compact.
- Complex Measure, Radon-Nikodym Theorem, Differentiation of an integral, Absolutely continuous of functions, Hahn decomposition Theorem, Product measure and Fubini Theorem.
- Fourier series and Fourier transform, theory.
- Theory of Distributions.

- Walter Rudin, Real and Complex Analysis, McGraw-Hill International Editions, Mathematics Series, McGraw-Hill Education (1987).
- Walter Rudin, Functional Analysis, Tata McGraw-Hill (1990). (for the Theory of Distributions)
- Halsey L. Royden, Real Analysis, Prentice Hall, Third Edition (1988).