Hausdorff dimension of intersections with planes and general sets
Pertti Mattila
University of Helsinki, Finland
![Hausdorff dimension of intersections with planes and general sets cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jfg-volume-8-issue-4.png&w=3840&q=90)
Abstract
We give conditions on a general family , , of orthogonal projections which guarantee that the Hausdorff dimension formula holds generically for measurable sets with positive and finite -dimensional Hausdorff measure, , and with positive lower density. As an application we prove for measurable sets with positive - and -dimensional measures, and with positive lower density that if , then for almost all rotations and for positively many .
Cite this article
Pertti Mattila, Hausdorff dimension of intersections with planes and general sets. J. Fractal Geom. 8 (2021), no. 4, pp. 389–401
DOI 10.4171/JFG/110