科研之友
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摘要
We consider a random version of the McMullen-Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an application, we discuss the issue on the intersection of the general Sierpinski carpet with its translations.
