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.