@article{Mahjoub2025, 
author = {Amal Mahjoub and Najmeddine Attia},
title = {On the study of general multifractal analysis of sets using vector-valued functions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {24469-24499},
keywords = {Hewitt-Stromberg measures, Hewitt-Stromberg dimensions, multifractal formalism, density results},
url = {https://www.sciopen.com/article/10.3934/math.20251085},
doi = {10.3934/math.20251085},
abstract = {In this work, we present a general approach to computing the Hewitt-Stromberg dimensions of a set    A in a metric space. This technique, originally introduced by Cutler and Tricot and later expanded by Ben Nasr et al., offers a generalization of classical dimension estimates and yields deeper understanding of the scaling behavior of measures in metric spaces. We applied this framework to binomial measures and developed a multifractal one for a function with respect to a gauge function    φ. Additionally, we explored the regularity of sets and measures by applying a tailored density theorem, extending existing results and offering novel insights into Moran sets.}
}