Some New Characterizations of Olsen's Multifractal Functions

被引：10
|
作者：
Selmi, Bilel [1 ]
机构：
[1] Univ Monastir, Anal Probabil & Fractals Lab LR18ES17, Dept Math, Fac Sci Monastir, Monastir 5000, Tunisia
来源：
RESULTS IN MATHEMATICS | 2020年 / 75卷 / 04期
关键词：
Multifractal Hausdorff and packing dimensions; multifractal dimensions of measures; multifractal analysis; SINGULARITY SPECTRUM; DIMENSION;
D O I：
10.1007/s00025-020-01277-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this work is to provide a representation of the multifractal Hausdorff and packing dimensions of compact sets in the Euclidean space in terms of the lower and upper local (q, mu)-dimensions of a probability measure on R-n, respectively. In addition, a relationship is established allowing to determine the Olsen's multifractal functions by means of the corresponding measures' versions. The multifractal functions are defined as the supremum over the lower and upper multifractal dimensions of all Borel probability measures.
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页数：16
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