Completeness of the space of separable measures in the Kantorovich-Rubinshteĭn metric
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911781375442944 |
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| author | Kravchenko, A. S. |
| author_facet | Kravchenko, A. S. |
| contents | We consider the space $M(X)$ of separable measures on the Borel $σ$-algebra ${\cal B}(X)$ of a metric space $X$. The space $M(X)$ is furnished with the Kantorovich-Rubinshteĭn metric known also as the ``Hutchinson distance''. We prove that $M(X)$ is complete if and only if $X$ is complete. We consider applications of this theorem in the theory of self-similar fractals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completeness of the space of separable measures in the Kantorovich-Rubinshteĭn metric Kravchenko, A. S. Metric Geometry Dynamical Systems 54E50 (Primary) 28C99 (Secondary) We consider the space $M(X)$ of separable measures on the Borel $σ$-algebra ${\cal B}(X)$ of a metric space $X$. The space $M(X)$ is furnished with the Kantorovich-Rubinshteĭn metric known also as the ``Hutchinson distance''. We prove that $M(X)$ is complete if and only if $X$ is complete. We consider applications of this theorem in the theory of self-similar fractals. |
| title | Completeness of the space of separable measures in the Kantorovich-Rubinshteĭn metric |
| topic | Metric Geometry Dynamical Systems 54E50 (Primary) 28C99 (Secondary) |
| url | https://arxiv.org/abs/2402.13935 |