Аннотация:
The problem on intersection of Cantor sets was examined in many papers. To solve this problem, we introduce the notion of lacunary self-similar set. The main difference to the standard (Hutchinson) notion of self-similarity is that the set of similarities used in the
construction may vary from step to step in a certain way. Using a modification of method described in [3], [4], we find the Hausdorff dimension of a lacunary self-similar set.
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