具有强分离条件的自相似集的最大密度（英文）  

Maximum Density for the Self-similar Set with the Strong Separation Condition

作　　者：许绍元[1] 周作领[2] 

机构地区：[1]韩山师范学院数学与统计学系,广东潮州521041 [2]中山大学岭南学院,广东广州510275

出　　处：《应用数学》2015年第3期517-523,共7页Mathematica Applicata

基　　金：Supported by the foundation of the research item of Strong Department of Engineering Innovation,which is sponsored by the Strong School of Engineering Innovation of Hanshan Normal University,China in 2013;National Natural Science Foundation of China(11371379)

摘　　要：本文证明对于满足强分离条件的自相似集E,存在一个闭凸集达到它的最大密度.即存在一个闭凸集V■E0(|V|>0),使得sup{μ(U)/|U|s:U■E0}=μ(V)/|V|s,其中U为闭集,E0表示自相似集E的闭凸壳,μ表示E上的唯一自相似概率测度.作为应用,我们给出命题"满足强分离开集条件的自相似集具有最优几乎处处覆盖"的一个新证明.We prove that there exists a closed convex set attaining the maximum density for the self-similar set E satisfying the strong separation condition. That is, there exists a closed convex set V C Eo, with ｜V｜ 〉 0, such that sup{μ（U）/｜U｜^s：U E0 is closed} =μ（U）/｜U｜^s, where E0 denotes the closed convex hull of the self-similar set E and μ denotes the unique self-similar probability measure on E. As a result, we give a new proof of the proposition that any self-similax set with the strong separation condition （SSC） admits an optional almost covering.

关 键 词：HAUSDORFF测度与维数 自相似集 强分离条件 最大密度 最优几乎处处覆盖 

分 类 号：O174.12[理学—数学]