**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

File translated from T

On 9 Apr 2003, 18:18.