Multifractal Geometry of Slices of Measures

  • Bilel Selmi

    Université de Monastir, Tunisia
Multifractal Geometry of Slices of Measures cover

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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 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. 237–253

DOI 10.4171/ZAA/1682