full
search.png

Search

close.png

Cancel

arrow
Volume 32, Issue 4
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

Anal. Theory Appl., 32 (2016), pp. 303-332.

Published online: 2016-10

Preview Full PDF 3268 37546

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • 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.

  • AMS Subject Headings

28A78, 28A80

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

anouar.benmabrouk@issatso.rnu.tn ( A. B. Mabrouk)

  • BibTex
  • RIS
  • TXT
@Article{ATA-32-303, author = {M. Menceur , A. B. Mabrouk , and Betina , K.}, title = {The Multifractal Formalism for Measures, Review and Extension to Mixed Cases}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {4}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n4.1}, url = {http://global-sci.org/intro/article_detail/ata/4673.html} }
TY - JOUR T1 - The Multifractal Formalism for Measures, Review and Extension to Mixed Cases AU - M. Menceur , AU - A. B. Mabrouk , AU - Betina , K. JO - Analysis in Theory and Applications VL - 4 SP - 303 EP - 332 PY - 2016 DA - 2016/10 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n4.1 UR - https://global-sci.org/intro/article_detail/ata/4673.html KW - 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. AB -

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.

M. Menceur, A. B. Mabrouk & K. Betina. (1970). The Multifractal Formalism for Measures, Review and Extension to Mixed Cases. Analysis in Theory and Applications. 32 (4). 303-332. doi:10.4208/ata.2016.v32.n4.1
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard