On the packing measure of slices of self-similar sets

Abstract

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.