分形集含有正Lebesgue测度与内部非空的等价性研究  

作　　者：罗伟杰 

机构地区：[1]华南理工大学,广东广州510641

出　　处：《科技风》2017年第25期176-177,共2页

摘　　要：Schief证明了若一个自相似集的自相似维数等于空间维数, 则该自相似集含有正Lebesgue测度等价于其含有内点. 本文基于Schief的结论, 证明了若有限个相似压缩簇对于同一个开集均满足开集条件, 并且各自的自相似维数均等于空间维数, 则由其生成的“ 弱” 不变集也含有内点.Schief demonstrated that tlie equality between the self - similar dimension of a self-similar set and the space dimension en-ures the equivalence of positive Lebesgue measure and nonempty interior. Based on Schief 3 s result,we prove that for finitely many iterated unction systems of contraction similitudes,if each of themsatisfies the open set condition with respect to the same open set,moreover,if each of them takes the space dimension as its similarity dimension,then the“weak” invariant set generated by them contains interiors.

关 键 词：自相似集 迭代函数系 开集条件 正Lebegue测度 内部非空 

分 类 号：O174.12[理学—数学]