The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

被引：0
|
作者：
Mohamed Menceur [1 ]
Anouar Ben Mabrouk [2 ,3 ]
Kamel Betina [1 ]
机构：
[1] Algerba and Number Theory Laboratory, Faculty of Mathematics, University of Sciences and Technology Houari Boumediene
[2] Computational Mathematics Laboratory, Department of Mathematics, Faculty of Sciences
[3] Department of Mathematics, HIgher Institute of Applied Mathematics and Informatics, Street of Assad Ibn Alfourat, Kairouan University
来源：
Analysis in Theory and Applications | 2016年 / 32卷 / 04期
关键词：
Hausdorff measures; packing measures; Hausdorff dimension; packing dimension; renyi dimension; multifractal formalism; vector valued measures; mixed cases; Holderian measures; doubling measures; Borel-Cantelli; large deviations;
D O I：
暂无
中图分类号：
O189 [拓扑（形势几何学）];
学科分类号：
070104 ;
摘要：
The multifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
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页码：303 / 332
页数：30
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