# Superdensity and infinitesimal Euclideanity of sets of finite perimeter

### (University of Trento)

**Event:** ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis

**Date:** Oct 07, 2013,
**time:** 15:30

**Abstract.** The rough idea that finite perimeter sets are "closer" to open sets than generic measurable sets with positive measure is confirmed by many facts (e.g. the decomposition properties, the constancy theorem, the path-connectedness). In this talk we furtherly develop such an idea by exposing some recent results concerning superdensity and infinitesimal Euclideanity of finite perimeter sets.