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arXiv · 1901.03834

On the projections of the multifractal packing dimension for q>1

Bilel Selmi
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Abstract

The aim of this article is to study the behaviour of the multifractal packing function $B_\mu(q)$ under projections in Euclidean space for $q>1$. We show that $B_\mu(q)$ is preserved under almost every orthogonal projection. As an application, we study the multifractal analysis of the projections of a measure. In particular, we obtain general results for the multifractal analysis of the orthogonal projections on $m$-dimensional linear subspaces of a measure $\mu$ satisfying the multifractal formalism.

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Bilel Selmi. 2019-01-12. On the projections of the multifractal packing dimension for q>1. https://doi.org/10.1007/s10231-019-00929-7

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