The Multifractal Formalism for Measures, Review and Extension to Mixed Cases
Year: 2016
Author: M. Menceur, A. B. Mabrouk, K. Betina
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 303–332
Abstract
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n4.1
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 303–332
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: 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.
Author Details
M. Menceur Email
A. B. Mabrouk Email
K. Betina Email
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