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arXiv · 2406.18863

The observable diameter of metric measure spaces and the existence of points of positive measures

Shun Oshima
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Abstract

A metric measure space is a metric space with a Borel measure. In Gromov's theory of metric measure spaces, there are important invariants called the partial diameter and the observable diameter. We obtain the result that the partial diameter or the observable diameter equals zero if and only if there exists a point that has positive measure.

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Shun Oshima. 2024-06-27. The observable diameter of metric measure spaces and the existence of points of positive measures. https://arxiv.org/abs/2406.18863

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