This course covers measure and integration. We start with abstract measures and their integration theory. Next, we construct the Lebesgue measure and follow it with a detailed study of Borel measures on locally compact Hausdorff spaces. Lp spaces and product measures along with Fubini’s theorem is taken up next. We finish with several classical reasul, Radon-Nikodym theorem, Ries representation theorem and Lebesgue differentiation theorem.
INTENDED AUDIENCE : First year MSc students in mathematics
PREREQUISITES : A course in real analysis and topology
INDUSTRY SUPPORT : Nil