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

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

A. B. Mabrouk

K. Betina

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