Tsukuba Journal of Mathematics

Distance between metric measure spaces and distance matrix distributions

Ryunosuke Ozawa

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Abstract

We study the Prohorov distance between the distance matrix distributions of two metric measure spaces. We prove that it is not smaller than 1-box distance between two metric measure spaces and also prove that it is not larger than 0-box distance between two metric measure spaces.

Article information

Source
Tsukuba J. Math., Volume 38, Number 2 (2015), 159-170.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1429103718

Digital Object Identifier
doi:10.21099/tkbjm/1429103718

Mathematical Reviews number (MathSciNet)
MR3336265

Zentralblatt MATH identifier
1321.53047

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 28D05: Measure-preserving transformations

Keywords
mm-space box distance function distance matrix distribution

Citation

Ozawa, Ryunosuke. Distance between metric measure spaces and distance matrix distributions. Tsukuba J. Math. 38 (2015), no. 2, 159--170. doi:10.21099/tkbjm/1429103718. https://projecteuclid.org/euclid.tkbjm/1429103718


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