REMARKS ON THE NONEXISTENCE OF DOUBLING MEASURES
REMARKS ON THE NONEXISTENCE OF DOUBLING MEASURES
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发表时间：
1999
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通讯作者：
E. Saksman
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作者：
E. Saksman
证明了存在关于欧氏距离不具有(非平凡)加倍测度的有界Jordan域Ω⊂Rn(n≥2).更一般地，证明了每一个没有孤立点的非空度量空间(X，d)都有一个开稠密子集A，使得(A，d)不具有加倍测度。
We establish that there are bounded Jordan domains Ω ⊂ R n ( n ≥ 2) that do not carrya (nontrivial) doubling measure with respect to the Euclidean distance. More generally , it is shown that everynonemptymetric space ( X, d) without isolated points has an open and dense subset A such that (A, d) does not carrya doubling measure.