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We construct new metric outer measures (multifractal analogues of the Hewitt-Stromberg measure) ${ H}^{q,t}_{\mu}$ and ${ P }^{q,t}_{\mu}$ lying between the multifractal Hausdorff measure ${\mathcal H}^{q,t}_{\mu}$ and the multifractal packing measure ${\mathcal P}^{q,t}_{\mu}$. We set up a necessary and sufficient condition for which multifractal Hausdorff and packing measures are equivalent to the new ones. Also, we focus our study on some regularities for these given measures. In particular, we try to formulate a new version of Olsen's density theorem when $\mu$ satisfies the doubling condition. As an application, we extend the density theorem given in \cite{HHBaek}.
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참고문헌 (29)
참고문헌 신청
Najmeddine Attia / 2018 / Relative multifractal spectrum / 대한수학회논문집 33(2):459~471
N. Attia / 2017 / Some density results of relative multifractal analysis / Chaos Solitons Fractals 103:1~11
H. K. Baek / 2008 / Regularities of multifractal measures / Proc. Indian Acad. Sci. Math. Sci 118(2):273~279
H. K. Baek / 2003 / Regularity of d-measure / Acta Math. Hungar 99(1-2):25~32
C. D. Cutler / 1995 / The density theorem and Hausdor inequality for packing measure in general metric spaces / Illinois J. Math 39(4):676~694
N. Attia / 2017 / Some density results of relative multifractal analysis / Chaos Solitons Fractals 103:1~11
H. K. Baek / 2008 / Regularities of multifractal measures / Proc. Indian Acad. Sci. Math. Sci 118(2):273~279
H. K. Baek / 2003 / Regularity of d-measure / Acta Math. Hungar 99(1-2):25~32
C. D. Cutler / 1995 / The density theorem and Hausdor inequality for packing measure in general metric spaces / Illinois J. Math 39(4):676~694
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