## Tsukuba Journal of Mathematics

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

### Distance between metric measure spaces and distance matrix distributions

#### 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