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April, 2019 The maximum of the 1-measurement of a metric measure space
Hiroki NAKAJIMA
J. Math. Soc. Japan 71(2): 635-650 (April, 2019). DOI: 10.2969/jmsj/78177817

Abstract

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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Hiroki NAKAJIMA. "The maximum of the 1-measurement of a metric measure space." J. Math. Soc. Japan 71 (2) 635 - 650, April, 2019. https://doi.org/10.2969/jmsj/78177817

Information

Received: 5 June 2017; Revised: 27 December 2017; Published: April, 2019
First available in Project Euclid: 19 March 2019

zbMATH: 07090059
MathSciNet: MR3943454
Digital Object Identifier: 10.2969/jmsj/78177817

Subjects:
Primary: 53C23
Secondary: 53C20

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 2 • April, 2019
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