Non-existence of multi-line Besicovitch sets
arXiv:1208.1877 · doi:10.5565/PUBLMAT_58114_10
Abstract
If a compact set K \subset R^2 contains a positive-dimensional family of line-segments in positively many directions, then K has positive measure.
7 pages. v2: corrected typos and added references, to appear in Publ. Mat