On the mutual singularity of multifractal measures

  • Received: 01 February 2020 Revised: 01 February 2020
  • Primary: 28A20; Secondary: 28A80

  • The aim of this article is to show that the multifractal Hausdorff and packing measures are mutually singular, which in particular provides an answer to Olsen's questions.

    Citation: Zied Douzi, Bilel Selmi. On the mutual singularity of multifractal measures[J]. Electronic Research Archive, 2020, 28(1): 423-432. doi: 10.3934/era.2020024

    Related Papers:

  • The aim of this article is to show that the multifractal Hausdorff and packing measures are mutually singular, which in particular provides an answer to Olsen's questions.



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    [1] Regularities of multifractal Hewitt-Stromberg measures. Commun. Korean Math. Soc. (2019) 34: 213-230.
    [2] N. Attia and B. Selmi, A multifractal formalism for Hewitt-Stromberg measures, Journal of Geometric Analysis, (2019). doi: 10.1007/s12220-019-00302-3
    [3] The validity of the multifractal formalism: results and examples. Adv. in Math (2002) 165: 264-284.
    [4] M. Das, Pointwise Local Dimensions, Ph.D. Thesis, The Ohio State University, 1996.
    [5] Hausdorff measures, dimensions and mutual singularity. Trans. Amer. Math. Soc. (2005) 357: 4249-4268.
    [6] A multifractal formalism. Adv. in Math. (1995) 116: 82-196.
    [7] The singularity spectrum $f(\alpha)$ of some Moranfractals. Monatsh Math. (2005) 144: 141-155.
    [8] Sequences of substitutions and related topics. Adv Math (China). (1989) 18: 270-293.
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