New fractal dimensions of measures and decompositions of singularly continuous measures

被引：16

作者：

Achour, Rim ^{[1
]}

Hattab, Jihed ^{[1
]}

Selmi, Bilel ^{[1
]}

机构：

[1] Univ Monastir, Fac Sci Monastir, Dept Math, Anal Probabil & Fractals Lab LR18ES17, Monastir 5000, Tunisia

来源：

FUZZY SETS AND SYSTEMS | 2024年 / 479卷

关键词：

ENTROPY;

D O I：

10.1016/j.fss.2024.108859

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

By introducing a novel expression for the Hausdorff and packing measures with respect to gauge functions, we establish a connection between different approaches to defining the exact Hausdorff and packing dimensions of measures. Furthermore, we define the upper and lower Hausdorff and packing dimensions of a Borel probability measure and demonstrate that these dimensions can be represented using an entropy formula. This paper also addresses an intriguing question raised multiple times regarding the structural representation of singular probability measures. We provide an affirmative response to this question by utilizing characteristic measures.

引用

页数：28

共 81 条

[1] How nature works: The science of self-organized criticality - Bak,P [J].