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

1 被引用数 (Scopus)

## 抄録

For a metric measure space, we consider the set of distributions of 1-Lipschitz functions, which is called the 1-measurement. On the 1-measurement, we have the Lipschitz order relation introduced by M. Gromov. The aim of this paper is to study the maximum and maximal elements of the 1-measurement of a metric measure space 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.

本文言語 English 635-650 16 Journal of the Mathematical Society of Japan 71 2 https://doi.org/10.2969/jmsj/78177817 Published - 2019

• 数学 (全般)

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