Math 5801

MATH5801 Measure Theory 4(3+1)

Rings, Algebra, σ-algebra, Monotone classes, Measure, elementary properties, outer measure, extension, completion and approximation theorems, Lebesgue’s measure, Lebesgue-Stieltje’s measure, measurable functions, integration with respect to a measure, the main theorems, the convergence of measurable functions, Radon-Nikodym theorem (absolutely continuous functions), FubiniTonelli theorem,Lp spaces: Holder and Minkowski inequalities, completeness of Lp spaces, Lp space as a Banach space, the dual of Lp space.

References:
1- H. L. Royden, Real Analysis. The Macmillan Company NewYork NY 1968.
2- Lawrence C Evans and Ronald F Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, London, UK, 1992.
3- Paul Halmos: Measure Theory, D.Van Norstand Company Inc, Princeton NJ, 1964. 
4- D. L. Cohn: Measure Theory, Birkhauser Boston Inc., Boston, MA, 1993.