Measure Theory

Code: MA550 | L-T-P-C: 3-1-0-8

Prerequisites: MA541 Real Analysis

Lebesgue outer measure, Lebesgue measurable sets, Lebesgue measure. Algebra and sigma-algebra of sets, Borel sets, Outer measures and measures, Caratheodory construction. Measurable functions, Lusin’s theorem, Egoroff’s theorem. Integration of measurable functions, Monotone convergence theorem, Fatou’s lemma, Dominated convergence theorem. Lp-spaces. Product measure, Fubini’s theorem. Absolutely continuous functions, Fundamental theorem of calculus for Lebesgue integral. Radon-Nikodym theorem. Riesz representation theorem

Texts:

1. G. de Barra: Measure Theory and Integration, New Age Publishers, 1st ed, 2013.
2. H. L. Royden & P. M. Fitzpatrick: Real Analysis, Pearson India, 2015

References:

1. D. L. Cohn: Measure Theory, Birkhauser, 1994
2. W. Rudin: Real and Complex Analysis, McGraw-Hill India, 2017
3. G. B. Folland: Real Analysis (2nd ed.), Wiley, 1999