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.
Citation
Tuomas Orponen. "Non-existence of multi-line Besicovitch sets." Publ. Mat. 58 (1) 213 - 220, 2014.
Information
Published: 2014
First available in Project Euclid: 20 December 2013
zbMATH: 1284.28004
MathSciNet: MR3161515
Subjects:
Primary:
28A80
Secondary:
28A78
,
42B25
Keywords:
Besicovitch sets
,
Kakeya maximal operator
Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques
