## Publicacions Matemàtiques

### Non-existence of multi-line Besicovitch sets

Tuomas Orponen

#### Abstract

If a compact set $K \subset \mathbb{R}^{2}$ contains a positive-dimensional family of line-segments in every direction, then $K$ has positive measure.

#### Article information

Source
Publ. Mat., Volume 58, Number 1 (2014), 213-220.

Dates
First available in Project Euclid: 20 December 2013