将格罗莫夫的 Lipschitz 秩扩展为带加性误差的 Lipschitz 秩

arXiv - MATH - Metric Geometry Pub Date : 2024-09-04 DOI:arxiv-2409.02459

Hiroki Nakajima

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引用次数: 0

摘要

格罗莫夫的利普齐茨阶是度量空间集合上的一种阶序关系。利用 Lipschitz 阶，可以构建具有集中拓扑的度量空间同构类空间的紧凑性。集中拓扑与度量集中现象密切相关。在本文中，我们将 Lipschitz 阶扩展为具有加性误差的 Lipschitz 阶，并证明了其有用的性质。我们还讨论了它与具有1-Lipschitz（直到加性误差）性质的映射的关系。

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Extension of Gromov's Lipschitz order to with additive errors

Gromov's Lipschitz order is an order relation on the set of metric measure spaces. One of the compactifications of the space of isomorphism classes of metric measure spaces equipped with the concentration topology is constructed by using the Lipschitz order. The concentration topology is deeply related to the concentration of measure phenomenon. In this paper, we extend the Lipschitz order to that with additive errors and prove useful properties. We also discuss the relation of it to a map with the property of 1-Lipschitz up to an additive error.

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arXiv - MATH - Metric Geometry

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