Syllabus

Measure spaces, Lebesgue measure, measurable functions and Lebesgue integral, Monotone convergence Theorem and Dominated convergence Theorem, relation between Riemann and Lebesgue integral. Product measures, Fubini’s Theorem. Lp spaces. Signed measures, Hahn decomposition, Radon-Nikodym Theorem. Convergence of sequences of measurable functions.

Course Outline