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

M. Menceur; A. B. Mabrouk; K. Betina

doi:10.4208/ata.2016.v32.n4.1

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

Authors

M. Menceur
A. B. Mabrouk
K. Betina

DOI:

https://doi.org/10.4208/ata.2016.v32.n4.1

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.

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.

Downloads

Published

2016-10-02

Abstract View

44823

Pdf View

4391

Issue

Vol. 32 No. 4 (2016)

Section

Articles

How to Cite

The Multifractal Formalism for Measures, Review and Extension to Mixed Cases. (2016). Analysis in Theory and Applications, 32(4), 303-332. https://doi.org/10.4208/ata.2016.v32.n4.1