### MA 5340 Measure and Integration

#### Course Details

Unit I: Review of Riemann Integral, Riemann-Stieltjes Integral.

Unit II: Lebesgue Measure; Lebesgue Outer Measure; Lebesgue Measurable Sets.

Unit III: Measure on an arbitrary sigma -Algebra; Measurable Functions; Integral of a Simple Measurable Function; Integral of Positive Measurable Functions.

Unit IV: Lebesgue's Monotone Convergence Theorem; Integrability; Dominated Convergence Theorem; Lp - Spaces. Differentiation and Fundamental theorem for Lebesgue integration.

Unit V: Product measure; Statement of Fubini's theorem.

#### Course References:

Text Books:

1. G. de Barra: Measure and Integration, Wiley Eastern, 1981.

2. H.L. Royden: Real Analysis, Third edition, Prentice-Hall of India, 1995.(Chapter 3, Sections 1-5)

3. W. Rudin: Real and Complex Analysis, Third edition, McGraw-Hill,International Editions, 1987. (Chapters 1, 3)

Reference:

1. I.K. Rana: An Introduction to Measure and Integration, Second Edition,Narosa, 2005.

2. D.L. Cohn: Measure Theory , Birkhauser, 1997.

3. P.K. Jain and V.P. Gupta: Lebesgue Measure and Integration, New Age International, 2006.