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arXiv · 1706.01258

The maximum of the 1-measurement of a metric measure space

Hiroki Nakajima
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Abstract

For a metric measure space, we treat the set of distributions of 1-Lipschitz functions, which is called the 1-measurement. On the 1-measurement, we have a partial order relation by the Lipschitz order introduced by Gromov. The aim of this paper is to study the maximum and maximal elements of the 1-measurement with respect to the Lipschitz order. We present a necessary condition of a metric measure space for the existence of the maximum of the 1-measurement. We also consider a metric measure space that has the maximum of its 1-measurement.

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Hiroki Nakajima. 2017-06-05. The maximum of the 1-measurement of a metric measure space. https://arxiv.org/abs/1706.01258

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