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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2402.13935 |
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Table des matières:
- 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.