一个关于上凸密度的公开问题的否定回答（英文）  

A Negative Answer to an Open Problem on Upper Convex Density

作　　者：尹建东[1] 聂饶荣[1] 周作领[2] 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]中山大学岭南学院,广东广州510275

出　　处：《应用数学》2014年第2期237-242,共6页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(11261039);the Natural Science Foundation of Jiangxi Province of China(20132BAB201009)

摘　　要：对于一个满足开集条件的自相似集E,本文得到如下有趣结论:如果E存在几乎处处最好覆盖{Ui}∞i=1,使得E-∪i≥1Ui是可数集,则E-E0是至多可数集,其中E0={x∈E|珡Ds c(E,x)=1}.作为应用,否定回答了周作领等在[周作领,瞿成勤,朱智伟.自相似集的结构———Hausdorff测度与上凸密度[M].北京:科学出版社,2008]中提出的一个公开问题.For a self-similar set E satisfying the open set condition,we prove an interesting result that if there exists an almost everywhere best covering {Ui）∞i=1 of E such that the set E-Ui≥1Ui is countable,then the set E--E0 is at most countable,where E0=（x∈E｜Dcs（E,x）=1）. As an applieation,we give a negative answer to the open problem posed by ZHOU Zuoling et. al in [ZHOU Zuoling, QU Chengqin,ZHU Zhiwei. The Structure of Self-similar Sets-Hausdorff Measure and Upper Convex Density. Beijing ： Sci ＆ Tec Press, 2008].

关 键 词：HAUSDORFF测度 自相似集 上凸密度 

分 类 号：O174.12[理学—数学]