Translator Disclaimer
2013 A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
Romain Abraham, Jean-François Delmas, Patrick Hoscheit
Author Affiliations +
Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-2116

Abstract

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the extended Gromov-Hausdorff-Prokhorov metric is a Polish space. This generalization is needed to define Lévy trees, which are (possibly unbounded) random real trees endowed with a boundedly finite measure.

Citation

Download Citation

Romain Abraham. Jean-François Delmas. Patrick Hoscheit. "A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces." Electron. J. Probab. 18 1 - 21, 2013. https://doi.org/10.1214/EJP.v18-2116

Information

Accepted: 24 January 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60004
MathSciNet: MR3035742
Digital Object Identifier: 10.1214/EJP.v18-2116

Subjects:
Primary: 60B05
Secondary: 05C80, ‎54E50‎

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.18 • 2013
Back to Top