Doubling measures with doubling continuous part
Doubling measures with doubling continuous part
复制标题
DOI：
10.1090/s0002-9939-10-10358-x
复制
发表时间：
2010-10
期刊：
影响因子：
--
通讯作者：
MAN-LI Lou;Min Wu
中科院分区：
文献类型：
--
作者：
MAN-LI Lou;Min Wu
我们证明，阳性Lebesgue度量的每个紧凑子集都具有不纯原子的双倍度量。另外，我们证明，对于每个紧凑而无孤立的点的密集子集，没有孤立的点，对于每个双倍的度量，上面都有一个可计数的集合，并在上面有一个加倍的度量。这表明有许多加倍措施的连续部分正在加倍。
We prove that every compact subset of of positive Lebesgue measure carries a doubling measure which is not purely atomic. Also, we prove that for every compact and nowhere dense subset of without isolated points and for every doubling measure on there is a countable set with and a doubling measure on such that . This shows that there are many doubling measures whose continuous part is doubling.