Every complete doubling metric space carries a doubling measure
Every complete doubling metric space carries a doubling measure
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DOI：
10.1090/s0002-9939-98-04201-4
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发表时间：
1998
影响因子：
3.9
通讯作者：
J. Luukkainen;E. Saksman
中科院分区：
文献类型：
--
作者：
J. Luukkainen;E. Saksman
我们证明，当X X倍增一倍并且更准确地说，X和X上的均匀度指数的同质性指数的INVIMA和X的同质性指数相等时，完整的度量空间X进行了加倍措施。我们还表明，RN的闭合子集X带有均匀性指数n的度量。这些结果基于由于Vol'berg和Konyagin引起的紧凑型X的情况。
We prove that a complete metric space X carries a doubling measure if and only if X is doubling and that more precisely the infima of the homogeneity exponents of the doubling measures on X and of the homogeneity exponents of X are equal. We also show that a closed subset X of Rn carries a measure of homogeneity exponent n. These results are based on the case of compact X due to Vol'berg and Konyagin.