Multifractal dimensions for projections of measures
Bilel Selmi
TL;DR
This paper investigates how the multifractal Hausdorff and packing dimensions of measures behave under orthogonal projections, aiming to refine existing results in multifractal analysis.
Contribution
It advances the understanding of multifractal dimensions of measures under projections, improving upon previous results by Dai.
Findings
Enhanced bounds for multifractal dimensions under projections
Refined analysis of multifractal exact dimension
Improved theoretical framework for multifractal measure analysis
Abstract
In this paper, we study the multifractal Hausdorff and packing dimensions of Borel probability measures and study their behaviors under orthogonal projections. In particular, we try through these results to improve the main result of M. Dai in \cite{D} about the multifractal analysis of a measure of multifractal exact dimension.
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