类切饼集上测度的局部维数存在的充要条件(英文)  

A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF LOCAL DIMENTION OF MEASURE ON COOKIE-CUTTER-LIKE SETS

作　　者：江登英[1] 

机构地区：[1]武汉理工大学理学院,湖北武汉430070

出　　处：《数学杂志》2009年第4期445-448,共4页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China (50872100);the Science and Technology Research Project of Ministry of Communications of China(2007-352-221-030)

摘　　要：本文研究了类切饼集上有限Borel正则测度的局部维数性质.利用中值定理和有界畸变原理,获得了一类类切饼集上测度的局部维数存在的一个充要条件,所获结果包含了已有结果.In this paper, we investigate the properties of local dimension of finite Borel regular measure on the cookie-cutter-like set. By using the mean value theorem and bounded distortion property, we obtain a necessary and sufficient condition for the existence of local dimension of measure on a class of cookie-cutter-like sets. The results obtained contain the corresponding results already known.

关 键 词：类切饼集 BOREL测度 局部维数 

分 类 号：O175.12[理学—数学]