Real Analysis

Measures and Integration.

Measures and Integration; Outer measure; Lesbegue Measure; Basic properties of Banach and Hilbert spaces; Operators; Duality; Basic theorems in functional analysis; Classical Banach spaces; Spectral theory of Operators in Hilbert spaces; L2-space as a Hilbert space; Banach algebras; Gelfand theory; compact operators; Examples and applications to classical analysis