Siberian Mathematical Journal

, Volume 47, Issue 1, pp 68–76

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

  • A. S. Kravchenko
Article

DOI: 10.1007/s11202-006-0009-6

Cite this article as:
Kravchenko, A.S. Sib Math J (2006) 47: 68. doi:10.1007/s11202-006-0009-6

Abstract

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.

Keywords

fractalsselfsimilar setinvariant measureseparable measureKantorovich-Rubinshtein metricHutchinson distance

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. S. Kravchenko
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia