Subject Code:  MA5L014 Subject Name: Measure Theory and Integration L-T-P: 3-1-0 Credit: 4
Pre-requisite(s): Real Analysis
Rings and Algebra, Monotone classes. Measures and outer measures. Measurable sets; Lebesgue Measure and its properties. Measurable functions and their properties, Convergence in measure. Integration: Sequence of integrable functions; Signed measures, Hahn and Jordan decomposition, Absolute continuity of measures, Radon-Nikodym theorem; Product measures, Fubini's theorem; Transformations and functions: The isomorphism theorem, Lp-spaces, Riesz-Fischer theorem; Riesz Representation theorem for L2 spaces, Dual of Lp-spaces; Measure and Topology: Baire and Borel sets, Regularity of Baire and Borel measures, Construction of Borel measures, Positive and bounded linear functionals.
Text Books:
  1. Royden  H.L. Real Analysis,  Macmillan
  2. De Barra  G. Measure Theory and Integration, New Age International
References:
  1. Halmos  P.R. Measure Theory, GraduateText in Mathematics, Springer-Verlag
  2. Cohn  D. L. Measure Theory, Springer
  3. Rana I. K.  An Introduction to Measure and Integration, Narosa Publishing House