[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2007.22.2.241

RELATION BETWEEN FRACTAL MEASURES AND CANTOR MEASURES

Baek, In-Soo (DEPARTMENT OF MATHEMATICS PUSAN UNIVERSITY OF FOREIGN STUDIES)

Publication Information

Communications of the Korean Mathematical Society / v.22, no.2, 2007 , pp. 241-246 More about this Journal

Abstract

We investigate the relation between Hausdorff(packing) measure and lower(packing) Cantor measure on a deranged Cantor set. If the infimum of some distortion of contraction ratios is positive, then Hausdorff(packing) measure and lower(packing) Cantor measure of a deranged Cantor set are equivalent except for some singular behavior for packing measure case. It is a generalization of already known result on the perturbed Cantor set.

Keywords

Cantor set; Hausdorff measure; packing measure; Cantor measure;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)
Times Cited By SCOPUS : 0

Reference
Cited By KSCI

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2	I. S. Baek, Dimensions of a deranged Cantor set with specific contraction ratios, Bull. Korean Math. Soc. 41 (2004), no. 2, 269-274 DOI ScienceOn
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4	K. J. Falconer, Techniques in fractal geometry, John Wiley and Sons, 1997
5	S. Meinershagen, Hausdorff and packing measure on a perturbed Cantor set, Real Analysis Exchange 27 (2002), no. 1, 177-190
6	I. S. Baek, Dimensions of the perturbed Cantor set, Real Analysis Exchange 19 (1994), no. 1, 269-273
7	I. S. Baek, Cantor dimension and its application, Bull. Korean Math. Soc. 41 (2004), no. 1, 13-18 DOI ScienceOn