Let be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension . Intersecting with translates of a fixed line, one can study the -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 -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