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Multifractal Analysis of Singularly Continuous Probability Measures

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Ukrainian Mathematical Journal Aims and scope

An Erratum to this article was published on 01 April 2006

Abstract

We analyze correlations between different approaches to the definition of the Hausdorff dimension of singular probability measures on the basis of fractal analysis of essential supports of these measures. We introduce characteristic multifractal measures of the first and higher orders. Using these measures, we carry out the multifractal analysis of singular probability measures and prove theorems on the structural representation of these measures.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    H. M. Torbin

  2. Kyiv National Pedagogic University, Kyiv, Ukraine

    H. M. Torbin

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  1. H. M. Torbin
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__________

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 706–720, May, 2005.

An erratum to this article is available at http://dx.doi.org/10.1007/s11253-006-0091-8.

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Torbin, H.M. Multifractal Analysis of Singularly Continuous Probability Measures. Ukr Math J 57, 837–857 (2005). https://doi.org/10.1007/s11253-005-0233-4

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  • DOI: https://doi.org/10.1007/s11253-005-0233-4

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