MA 813, Measure Theory - Fall 2025
MA 813, Measure Theory - Fall 2025
Instructor : Chandan Biswas
Office : 202 F, Mathematics Department
Office Phone : +91 2225767485
Email : cbiswas@iitb.ac.in (if you don't hear back within 48 hours please send a reminder)
Schedule : The class meets twice each week, Tuesday/Friday, 5:30 - 6:55 pm.
Office Hours : Tuesday 4:30 - 5:30 pm.
Textbook : K. Chandrasekharan, A Course on Topological Groups, Hindustan Book Agency, 1996.
L. Nachbin, The Haar Integral, van Nostrand, 1965.
I. K. Rana, An Introduction to Measure and Integration, 2nd Ed., American Mathematical Society, 2002.
H. L. Royden, Real Analysis, 3rd Ed., Prentice Hall of India, 1988.
W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987.
Syllabus :
Review of measure theory: monotone convergence theorem, dominated convergence theorem, complete measures. Borel measures: Riesz representation theorem, Lebesgue measure on Rk, Lp spaces302225 Complex measures: total variation, absolute continuity, Radon-Nikodym theorem, polar and Hahn decompositions, bounded linear functionals on Lp, generalised Riesz representation theorem.302225 Differentiation: Maximal function, Lebesgue points, absolute continuity of functions, fundamental theorem of calculus, Jacobian of a differentiable transformation, change of variable formula.302225 Product measures: Fubini`s theorem, completion of product measures, convolutions, Fourier transform, Riemann-Lebesgue lemma, inversion theorem, Plancherel theorem, L1 as a Banach algebra.302225 Content on a locally compact Hausdorff space, existence and uniqueness of the Haar measure on a locally compact group.
Course Policy
You are encouraged to attend lectures regularly. You should try to read the book/class notes and do all of the problems. All the relevant class materials and announcements will be posted on the webpage. Please feel free to ask questions during the class and office hours.
Please Note
A pink slip is a must if asking for a make up exam.
No calculators are allowed in the exams.
Grading :
Midterm : 30%
Final exam : 70%.