Journal of Fractal Geometry

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Volume 2, Issue 4, 2015, pp. 389–401
DOI: 10.4171/JFG/26

Published online: 2015-08-31

On the packing measure of slices of self-similar sets

Tuomas Orponen[1]

(1) University of Helsinki, Finland

Let $K \subset \mathbb R^{2}$ be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension $\mathrm {dim} \: K = s > 1$. Intersecting $K$ with translates of a fixed line, one can study the $(s - 1)$-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 $(s - 1)$-dimensional packing measure under relatively mild assumptions.

Keywords: Self-similar sets, slicing, packing measures

Orponen Tuomas: On the packing measure of slices of self-similar sets. J. Fractal Geom. 2 (2015), 389-401. doi: 10.4171/JFG/26