On the Hausdorff and packing measures of slices of dynamically defined sets

  • Ariel Rapaport

    The Hebrew University of Jerusalem, Israel

Abstract

Let be integers, and let be a self-similar set satisfying the strong separation condition, and with dim . We study the a.s. values of the -dimensional Hausdorff and packing measures of , where is a typical -dimensional affine subspace.

For let be the attractor of the IFS , where and for each . We show that for certain numbers , for instance and , if , then typically we have .

Cite this article

Ariel Rapaport, On the Hausdorff and packing measures of slices of dynamically defined sets. J. Fractal Geom. 3 (2016), no. 1, pp. 33–74

DOI 10.4171/JFG/29