Multifractal Geometry of Slices of Measures

Abstract

The aim of this article is to study the behavior of the multifractal packing function under slices in Euclidean space. We discuss the relationship between the multifractal packing and pre-packing functions of a compactly supported Borel probability measure and those of slices or sections of the measure. More specifically, we prove that if $\mu$ satisfies a certain technical condition and $q$ lies in a certain somewhat restricted interval, then Olsen's multifractal dimensions satisfy the expected adding of co-dimensions formula.