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
Download PDF

This article is published open access under our Subscribe to Open model.

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