剪切集的上盒维数的一种等价刻画  

An equivalent definition of the upper box dimension of cut-out sets

作　　者：殷峰丽[1] 王聪[2] YIN Fengli WANG Cong(School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001 School of Mathematics and Statistics, Central China Normal University, Wuhan 430079)

机构地区：[1]周口师范学院数学与统计学院,河南周口466001 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2016年第5期649-651,共3页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金面上项目(11271148)

摘　　要：该文给出了直线上剪切集的上盒维数的一种等价刻画,即dimB(E)=inf{s>0:αs m<m=1∞},其中{Ai}i≥1为剪切集E的间隔序列.对于高维空间中集合E若满足logδliminf k=1,以及k→∞logδk+1E(δk)的每一个连通分支的勒贝格测度都小于Cδd k,其中C为常数、{δk}k≥1为一个趋向于0的序列,我们的结论也是成立的.In the present work,an equivalent definition of the upper box dimension of∞cut-out sets is generated,as dimB（E）=inf{s〉0：∞∑m=1 sα m〈∞},where {Ai }i≥1is the gap m=1sequence of cut-out set E.The conclusion remains true in higher dimension for set E logδwhich satisfies that liminf k=1and every connected component of E（δk）has Lebek→∞logδk＋1sgue measure less than Cδd k,when there exist a constantCand a sequence {δk }k≥1tending to 0.

关 键 词：剪切集 上盒维数 间隔序列 

分 类 号：O192[理学—数学]