JournalsjfgVol. 2 , No. 4pp. 389–401

On the packing measure of slices of self-similar sets

  • Tuomas Orponen

    University of Helsinki, Finland
On the packing measure of slices of self-similar sets cover
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Abstract

Let KR2K \subset \mathbb R^{2} be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension dimK=s>1\mathrm {dim} \: K = s > 1. Intersecting KK with translates of a fixed line, one can study the (s1)(s - 1)-dimensional Hausdorff and packing measures of the generic non-empty line sections. In a recent article, T. Kempton gave a necessary and sufficient condition for the Hausdorff measures of the sections to be positive. In this paper, I consider the packing measures: it turns out that the generic section has infinite (s1)(s - 1)-dimensional packing measure under relatively mild assumptions.

Cite this article

Tuomas Orponen, On the packing measure of slices of self-similar sets. J. Fractal Geom. 2 (2015), no. 4 pp. 389–401

DOI 10.4171/JFG/26