Advanced Analysis

In the class we will discuss several advances topics in Real Analysis. Among the topics that will be covered there are:

1. Abstract measure theory.
2. Carathéodory construction of measures.
3. Hausdorff Measures.
4. Covering theorems and derivation of measures.
5. Differentiability properties of Lipschitz functions.
6. Kirszbraun extension theorem for Lipschitz functions.
7. Area and Coarea formulas.
8. Basic properties of Rectifiable sets.

Date and time info
Wednesday 11.15 - 12.45

Keywords
Real Analysis, Measure and Integration Theory, Rectifiability

Prerequisites
Analysis I, II, III and basics of functional analysis

Language
English