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Separation properties for self-similar sets. (English) Zbl 0807.28005
Summary: Given a self-similar set $$K$$ in $$\mathbb{R}^ s$$ we prove that the strong open set condition and the open set condition are both equivalent to $$H^ \alpha(K)> 0$$, where $$\alpha$$ is the similarity dimension of $$K$$ and $$H^ \alpha$$ denotes the Hausdorff measure of this dimension. As an application we show for the case $$\alpha= s$$ that $$K$$ possesses inner points iff it is not a Lebesgue null set.

##### MSC:
 28A78 Hausdorff and packing measures 28A80 Fractals
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##### References:
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