Hausdorff dimension and measure of a class of subsets of the general Sierpinski carpets

Authors
Citation
Gui, Yong Xin, Hausdorff dimension and measure of a class of subsets of the general Sierpinski carpets, Acta mathematica Sinica. English series (Print) , 26(7), 2010, pp. 1369-1382
ISSN journal
14398516
Volume
26
Issue
7
Year of publication
2010
Pages
1369 - 1382
Database
ACNP
SICI code
Abstract
In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions with proportional frequency. We calculate the Hausdorff and Box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.