Measure and integration (MA 222) (Jan-Apr 2018)Tue, Thu 2:00-3:30, LH-4, Mathematics department
Tutorials by Sumit Mohanty: Day TBA, Time TBA LH-1, Mathematics department.
Description: This is a course in measure theory. The official syllabus reads:
Construction of Lebesgue measure, Measurable functions, Lebesgue integration, Abstract measure and abstract integration, Monotone convergence theorem, Dominated convergence theorem, Fatou’s lemma, Comparison of Riemann integration and Lebesgue integration, Product sigma algebras, Product measures, Sections of measurable functions, Fubini’s theorem, Signed measures and Randon-Nikodym theorem, Lp-spaces, Characterization of continuous linear functionals on Lp - spaces, Change of variables, Complex measures, Riesz representation theorem.
The actual coverage of topics may differ slightly due to constraints of time and taste.
Grading: The final grade will be based on homeworks (may be) and midterms (total of 50%) and the final exam (50%). Solving problems (preferably many more than given in the problem sets) is absolutely crucial to develop an understanding of the subject.
Texts and other resources: There are many books on the subject. The following appear to be well-written or interesting in other ways.
A list of problems