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

## TL;DR

This paper investigates how the multifractal packing dimension of a measure behaves under orthogonal projections in Euclidean space for q>1, showing it is preserved in almost all cases and applying this to multifractal analysis of projections.

## Contribution

It demonstrates the preservation of the multifractal packing dimension under almost all orthogonal projections and applies this to analyze the multifractal properties of projected measures.

## Key findings

- $B_(q)$ is preserved under almost every orthogonal projection.
- Provides general results for multifractal analysis of projections of measures.
- Applies findings to measures satisfying the multifractal formalism.

## 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.