Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 13-18 Printed March 1, 2004
In-Soo Baek Pusan University of Foreign Studies
Abstract : We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.
Keywords : weak local dimension, deranged Cantor set, Hausdorff dimension, packing dimension