Completeness of the Space of Separable Measures in the Kantorovich-Rubinshtein Metric
- Cite this article as:
- Kravchenko, A.S. Sib Math J (2006) 47: 68. doi:10.1007/s11202-006-0009-6
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 ). 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.