Multifractal dimensions for projections of measures

Author:

Selmi Bilel1ORCID

Affiliation:

1. Faculty of Sciences of Monastir

Abstract

In this paper, we calculate 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.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference49 articles.

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2. N. Attia, B. Selmi and Ch. Souissi. Some density results of relative multifractal analysis. Chaos, Solitons & Fractals. 103 (2017), 1-11. https://doi.org/10.1016/j.chaos.2017.05.029

3. I. S. Baek. On deranged Cantor sets. Kyungpook Math. Journal. 38 (1998), 363-367.

4. I. S. Baek. Weak local dimension on deranged Cantor sets. Real Analysis Exchange. 26 (2001), 553-558. https://doi.org/10.2307/44154059

5. I. S. Baek. Multifractal by self-similar measures. J. Appl. Math. & Computing., 23 (2007), 497-503.

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