Non-existence of multi-line Besicovitch sets

Tuomas Orponen

doi:pm/1387570397

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Home > Journals > Publ. Mat. > Volume 58 > Issue 1 > Article

2014 Non-existence of multi-line Besicovitch sets

Tuomas Orponen

Publ. Mat. 58(1): 213-220 (2014).

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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.