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

作　　者：Mohamed Menceur Anouar Ben Mabrouk Kamel Betina 

机构地区：[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

出　　处：《Analysis in Theory and Applications》2016年第4期303-332,共30页分析理论与应用（英文刊）

摘　　要：The mulfifractal 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.The mulfifractal 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.

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 

分 类 号：O189[理学—数学]