Volume 32, Issue 4
The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

M. Menceur, A. Mabrouk & K. Betina

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

Published online: 2016-10

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  • 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

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@Article{ATA-32-303, author = {M. Menceur, A. Mabrouk and K. Betina}, 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, A. Mabrouk & K. Betina 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 KW - packing measures KW - Hausdorff dimension KW - packing dimension KW - renyi dimension KW - multifractal formalism KW - vector valued measures KW - mixed cases KW - Holderian measures KW - doubling measures KW - Borel-Cantelli KW - 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. 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
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