J. Korean Math. Soc. 2004; 41(5): 933-944
Printed September 1, 2004
Copyright © The Korean Mathematical Society.
In-Soo Baek
Pusan University of Foreign Studies
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 R\'enyi 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
MSC numbers: 28A78, 60B05
2014; 51(5): 1075-1088
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd