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Indian Institute of Science Education and Research Bhopal


MTH 603:  Real Analysis (4)

Several variable calculus: A quick overview, the contraction mapping theorem, the inverse function theorem, the implicit function theorem.
Riemann integration in Rn, n≥1.

Lebesgue measure and integration: Measures, measurable functions, integration of nonnegative and complex functions, modes of convergence, convergence theorems, product measure, Fubini's theorem, convolution, integration in polar coordinates.

Signed measures and differentiation, complex measures, total variation, absolute continuity, Fundamental theorem of calculus for Lebesgue integral, the Radon-Nikodym theorem and consequences.

Lp spaces, the Hölder and Minkowski inequalities, Jensen's inequality, completeness, the Riesz representation theorem, dual of Lp spaces.

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