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Non-existence of multi-line Besicovitch sets

Tuomas Orponen

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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

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

First available in Project Euclid: 20 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Besicovitch sets Kakeya maximal operator


Orponen, Tuomas. Non-existence of multi-line Besicovitch sets. Publ. Mat. 58 (2014), no. 1, 213--220.

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