@article{Mahjoub2025, 
author = {Amal Mahjoub and Najmeddine Attia},
title = {On the study of multifractal analysis of functions in a metric space},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {25011-25032},
keywords = {multi-fractal formalism, Hausdorff and packing measures, Hausdorff and packing dimensions},
url = {https://www.sciopen.com/article/10.3934/math.20251108},
doi = {10.3934/math.20251108},
abstract = {Multi-fractal analysis plays a crucial role in understanding the complex behaviors of functions across different fields. In this study, we presented an innovative approach to examining the multi-fractal formalism. Specifically, we introduced new multi-fractal Hausdorff and packing measures, enabling the exploration of the multi-fractal spectrum within a metric space and offering a novel proof that extended the classical results in this setting. As an application, we focused on the Birkhoff averages when the multi-fractal formalism did not hold.}
}