The maximum of the 1-measurement of a metric measure space
キーワード:
metric measure space,
Lipschitz order,
1-measurement,
isoperimetric inequality,
observable diameter
2019 年 71 巻 2 号 p. 635-650
詳細
2019 年 71 巻 2 号 p. 635-650
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.
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