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

Bilel Selmi

Abstract


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.


Keywords


Multifractal measures; Hausdorff measure; packing measure; regularity; densities.

Subject classification

28A78, 28A80.

Sponsor(s)



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References


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