DOUBLING MEASURES WITH DOUBLING CONTINUOUS PART

被引:5
|
作者
Lou, Man-Li [1 ]
Wu, Min [1 ]
机构
[1] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China
基金
中国国家自然科学基金;
关键词
doubling measure; purely atomic; continuous part;
D O I
10.1090/S0002-9939-10-10358-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that every compact subset of R-d of positive Lebesgue measure carries a doubling measure which is not purely atomic. Also, we prove that for every compact and nowhere dense subset E of R-d without isolated points and for every doubling measure mu on E there is a countable set F with E boolean AND F = empty set and a doubling measure nu on E boolean OR F such that nu vertical bar(E) = mu. This shows that there are many doubling measures whose continuous part is doubling.
引用
收藏
页码:3585 / 3589
页数:5
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