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SUBSETS OF THE GENERAL SIERPINSKI CARPET WITH MIXED GROUP FREQUENCIES

YONGXIN GUI

Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

Department of Mathematics, Xianning College, Xianning 437005, P. R. China

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and

WENXIA LI

Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

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https://doi.org/10.1142/S0129167X09005765Cited by:0 (Source: Crossref)

Abstract

We consider a class of subsets of the general Sierpinski carpet which is characterized by insisting that the allowed digits in the expansion occur with prescribed mixing group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive and finite.

Keywords:

AMSC: 28A80, 28A78

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