Relation between fractal measures and Cantor measures
Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 241-246 Printed June 1, 2007
In-Soo Baek Pusan University of Foreign Studies
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 mea-sure