Orponen, Tuomas Non-existence of multi-line Besicovitch sets. (English) Zbl 1284.28004 Publ. Mat., Barc. 58, No. 1, 213-220 (2014). Summary: 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. MSC: 28A80 Fractals 28A78 Hausdorff and packing measures 42B25 Maximal functions, Littlewood-Paley theory Keywords:Besicovitch sets; Kakeya maximal operator PDFBibTeX XMLCite \textit{T. Orponen}, Publ. Mat., Barc. 58, No. 1, 213--220 (2014; Zbl 1284.28004) Full Text: DOI arXiv Euclid