Completeness of the Space of Separable Measures in the Kantorovich-Rubinshtein Metric

被引：0
|
作者：
A. S. Kravchenko
机构：
[1] Sobolev Institute of Mathematics,
来源：
Siberian Mathematical Journal | 2006年 / 47卷
关键词：
fractals; selfsimilar set; invariant measure; separable measure; Kantorovich-Rubinshtein metric; Hutchinson distance;
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学科分类号：
摘要：
We consider the space M(X) of separable measures on the Borel σ-algebra ℬ(X) of a metric space X. The space M(X) is furnished with the Kantorovich-Rubinshtein metric known also as the “Hutchinson distance” (see [1]). We prove that M(X) is complete if and only if X is complete. We consider applications of this theorem in the theory of selfsimilar fractals.
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页码：68 / 76
页数：8
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