MTL510
| MTL510 | |
|---|---|
| Measure and Integration | |
| Credits | 4 |
| Structure | 3-1-0 |
| Pre-requisites | |
| Overlaps | |
MTL510 : Measure and Integration
[edit]Outer measures, measures and measurable sets, Lebesgue measure on R, Borel measure Measurable functions, simple functions, Egoroff's theorem, Lebesgue integral and its properties, monotone convergence theorem, Fatou's Lemma, Dominated convergence theorem various modes of convergence and their relations Signed measures, Hahn and Jordan decomposition theorems, Lebesgue-Radon-Nikodym theorem, Lebesgue decomposition theorem, the representation of positive linear functionals on C c(X) Product measures, iterated integrals, Fubini's and Tonelli's theorems Lp spaces and their completeness, conjugate space of Lp for 1 < p< infinity, conjugate space of L1 for sigma-finite measure space Differentiation of monotone functions, functions of bounded variation, differentiation of an integral, absolute continuity.