关于自相似集的一个维数定理

A Theorem on the Dimensions of Self-Similar Sets

本文对严格自相似集，提出了一个比“开集”条件更弱的“可解”条件，并且证明：在可解条件下，自相似集的Ｈａｕｓｄｏｒｆｆ维数及Ｂｏｕｌｉｇａｎｄ维数与其相似维数一致．

In this paper , we propose a“resoluable condition”that is weaker than“open setcondition”for (strict)self-similar set, and prove that under“resoluable condition”,the Hausdorffand Bonligand dimensionof a self-similar set is identical with its similar dimension,