| Course Description : | Measure spaces, outer measure, Borel measures, integration, modes of convergence, convergence theorems of Lebesgue integral, product measures, signed measures, absolutely continuous measures, the Lebesgue-Radon-Nikodym theorem, the Lebesgue-Radon-Nikodym derivative, complex measures, Locally integrable, Hardy-Littlewood maximal function, the maximal theorem, the Lebesgue differentiation theorem, Basic theory of Lp-spaces, the dual of Lp-spaces, distribution functions and weak Lp-spaces, and Radon Measures.
Textbook: Folland, G. B. (1999). Real Analysis: Modern Techniques and Their Applications, 2nd Edition, Wiley, USA.
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