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2014 Non-existence of multi-line Besicovitch sets
Tuomas Orponen
Publ. Mat. 58(1): 213-220 (2014).

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.

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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

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Vol.58 • No. 1 • 2014
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