MA51002: Measure Theory And Integration
| MA51002 | |||||||||||||||||||||||||||||
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| Course name | Measure Theory And Integration | ||||||||||||||||||||||||||||
| Offered by | Mathematics | ||||||||||||||||||||||||||||
| Credits | 4 | ||||||||||||||||||||||||||||
| L-T-P | 3-1-0 | ||||||||||||||||||||||||||||
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| Semester | Spring | ||||||||||||||||||||||||||||
Syllabus
Syllabus mentioned in ERP
Prerequisite: Real Analysis Algebra of sets, ring, sigma-ring, field and sigma field of sets, monotone class, Lebesgue measure and outer measure, measurable sets, measurable functions, Littlewoods three principles, existence of non-measurable set. Lebesgue integral of a bounded function over a set of finite measure, the integral of a non-negative function, general Lebesgue integral, convergence in measure, functions of bounded variation, absolute continuity, differentiation and integration, general measure and integration, signed measure, Hahn-Jordan decomposition, Radon-Nikodym and Lebesgue decomposition theorems, product measures and Fubinis theorem. Lp spaces, Minkowski and Holder inequalities, convergence and completeness approximation in Lp , bounded linear functionals on Lp spaces.