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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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참고문헌 (26)
참고문헌 신청
N. Attia / 2017 / Some density results of relative multifractal analysis / Chaos, Solitons and Fractals 103:1~11
H.K. Baek / 2003 / Regularity of d-measure / Acta Math. Hungarica 99:25~32
H.K. Baek / 2008 / Regularities of multifractal measures / Proc. Indian Acad. Sci. 118:273~279
A. S. Besicovitch / 1938 / On the fundamental geometrical properties of linearly measur-able plane sets of points II / Math. Ann. 155:296~329
J. Cole / 2003 / Multifractal Variation Measures and Multifractal Density Theorems / Real Analysis Exchange 28:501~514
H.K. Baek / 2003 / Regularity of d-measure / Acta Math. Hungarica 99:25~32
H.K. Baek / 2008 / Regularities of multifractal measures / Proc. Indian Acad. Sci. 118:273~279
A. S. Besicovitch / 1938 / On the fundamental geometrical properties of linearly measur-able plane sets of points II / Math. Ann. 155:296~329
J. Cole / 2003 / Multifractal Variation Measures and Multifractal Density Theorems / Real Analysis Exchange 28:501~514
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