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 satisfies a certain technical condition and lies in a certain somewhat restricted interval, then Olsen's multifractal dimensions satisfy the expected adding of co-dimensions formula.
Cite this article
Bilel Selmi, Multifractal Geometry of Slices of Measures. Z. Anal. Anwend. 40 (2021), no. 2, pp. 237–253DOI 10.4171/ZAA/1682