Publicacions Matemàtiques

Non-existence of multi-line Besicovitch sets

Tuomas Orponen

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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

Permanent link to this document
https://projecteuclid.org/euclid.pm/1387570397

Mathematical Reviews number (MathSciNet)
MR3161515

Zentralblatt MATH identifier
1284.28004

Subjects
Primary: 28A80: Fractals [See also 37Fxx]
Secondary: 28A78: Hausdorff and packing measures 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Besicovitch sets Kakeya maximal operator

Citation

Orponen, Tuomas. Non-existence of multi-line Besicovitch sets. Publ. Mat. 58 (2014), no. 1, 213--220. https://projecteuclid.org/euclid.pm/1387570397


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