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Abstract. We consider a class of subsets of the general Sierpinski carpet which are characterized by insisting that the allowed digits in the expansion occur with prescribed group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive finite.
AMS Subject Classification
(1991): 28A80, 28A78
Keyword(s):
Hausdorff dimension,
Sierpinski carpets,
Hausdorff measure
Received July 4, 2007, and in revised form September 16, 2008. (Registered under 20/2007.)
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