Duration: 21 weeks

Number of lectures per week: 3

Assessment: Regular assignments.

End-of-year Examination: One 3-hour examination

Description:

Measure theory

Measurable sets and functions, definitions and properties of the integral. Convergence theorems. Carathéodory extension theorem. Sigma measures, decompositions and the Radon-Nikodym theorem. Fubini theorem.

Banach Spaces

Bounded linear maps, finite dimensional spaces, quotient spaces, Hahn-Banach theorem, dual spaces, Riesz representation theorem, Stone-Weierstrass theorem, open mapping theorem, closed graph theorem.

Hilbert spaces

Orthonormal bases, orthogonal projection, self-adjoint and normal operators.

Apr 9, 2003