Self-similar and self-affine sets; measure of the intersection of two copies
Self-similar and self-affine sets; measure of the intersection of two copies
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发表时间：
2007-04
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通讯作者：
Márton Elekes;T. Keleti;A. M'ath'e
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作者：
Márton Elekes;T. Keleti;A. M'ath'e
设K是R^d中的自相似或自仿射集，\mu是其上的自相似或自仿射测度，G是R^d的仿射映射群、相似群、等距群或平移群。在各种假设下（例如分离条件或我们假设变换是小扰动或K是所谓的Sierpinski海绵），我们证明了以下类型的定理，它们彼此密切相关;不稳定性：存在常数c 0，我们还得到了关于$g$的结果，其中$g（K）\su K$或$g（K）\supset K$ holds。
Let K be a self-similar or self-affine set in R^d, let \mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation conditions or we assume that the transformations are small perturbations or that K is a so called Sierpinski sponge) we prove theorems of the following types, which are closely related to each other; Non-stability: There exists a constant c 0, and we also get results about those $g$'s for which $g(K)\su K$ or $g(K)\supset K$ holds.