MA 4080: Measure and Integration
Class timings:
XXday: XX:00 am to XX:00 am
XXday: XX:00 am to XX:00 am
XXday: XX:00 am to XX:00 am
Examination and Grades:
The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.
Syllabus:
Sigma-algebra of measurable sets. Completion of a measure. Lebesgue Measure and its properties. Non-measurable sets.
Measurable functions and their properties. Integration and Convergence theorems. Lebesgue integral, Functions of bounded variation and absolutely continuous functions.
Fundamental Theorem of Calculus for Lebesgue Integrals.
Product measure spaces, Fubini's theorem. L^p-spaces, duals of L^p spaces. Riesz representation theorem for C([a,b]).
References:
- H. L. Royden, Real analysis. Third edition. Macmillan Publishing Company, New York, 1988.
- W. Rudin, Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.
- G. B. Folland, Real Analysis; Modern Techniques and Their Applications (Second Edition)
- K. R. Parthasarathy, Introduction to Probability and Measure, TRIM Series, Vol .33, Hindustan book agency, New Delhi, 2005.
- Krishna B. Athreya and S. Lahiri, Measure theory and probability theory. Springer Texts in Statistics, Springer Verlag, 2006.