[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2004.41.5.933

PACKING DIMENSION OF MEASURES ON A RANDOM CANTOR SET

Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)

Publication Information

Journal of the Korean Mathematical Society / v.41, no.5, 2004 , pp. 933-944 More about this Journal

Abstract

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.

Keywords

packing dimension; random Cantor set;

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