• Korean Journal of Mathematics
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• v.12 no.1
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• pp.1-5
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• 2004

We study Hausdorff and packing dimensions of subsets of a coding space with an ultra metric from a multifractal spectrum induced by a self-similar measure on a Cantor set using a function satisfying a H$\ddot{o}$lder condition.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.157-163
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• 2008

Using informations of subsets of divergence points and the relation between members of spectral classes, we give another complete decomposition of spectral classes generated by lower(upper) local dimensions of a self-similar measure on a self-similar Cantor set with full information of their dimensions. We note that it is a complete refinement of the earlier complete decomposition of the spectral classes. Further we study the packing dimension of some uncountable union of distribution sets.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.221-226
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• 2015

The natural projection of a parameter lower (upper) distribution set for a self-similar measure on a self-similar set satisfying the open set condition is the cylindrical lower or upper local dimension set for the Legendre self-similarmeasure which is derived from the self-similar measure and the self-similar set.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1073-1097
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• 2022

In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure 𝓗^q,t_𝜇 and multifractal packing measure 𝓟^q,t_𝜇 of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in [34]. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in [35], by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.1-5
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• 2007

We study the topological magnitude of a special subset from the distribution subsets in a self-similar Cantor set. The special subset whose every element has no accumulation point of a frequency sequence as some number related to the similarity dimension of the self-similar Cantor set is of the first category in the self-similar Cantor set.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.733-738
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• 2008

Using an information of dimensions of divergence points, we give full information of dimensions of the completely decomposed class of the lower(upper) distribution sets of a self-similar Cantor set. Further using a relationship between the distribution sets and the subsets generated by the lower(upper) local dimensions of a self-similar measure, we give full information of dimensions of the subsets by the local dimensions.