Korean J. Math. Vol. 26 No. 2 (2018) pp.271-283
DOI: https://doi.org/10.11568/kjm.2018.26.2.271

Some results about the regularities of multifractal measures

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Bilel Selmi


In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in \big(Proc. Indian Acad. Sci. (Math. Sci.) Vol. {\bf118}, (2008), pp. 273-279.\big). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.

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