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

- Construction of Lebesgue measure, Measurable functions, Lebesgue integration.
- Monotone convergence theorem, dominated convergence theorem, Fatou’s lemma
- Comparison of Riemann integration and Lebesgue integration
- Lp(Rn) spaces (completeness, dense subsets, notion of separability)
- Product sigma algebras, Product measures, Fubini’s theorem in Rn(at least statement with examples)
- Characterisation of continuous linear functionals on Lp spaces.
- Functions of bounded variation, Absolutely continuous functions, Fundamental
theorem of Calculus

bstract measures and integration, signed measure, Radon
Nikodym theorem, complex measures, Riesz representation theorem

- Stein and Shakarchi: Real analysis (Measure theory and integration.
- W. Rudin: Real and Complex Analysis
- G. B. Folland: Real Analysis, Modem techniques and their applications
- H.L. Royden: Real Analysis
- R. Wheeden and A. Zygmund: Measure and Integral: An introduction to Real
Analysis.