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A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces

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1.	Title	Title of document	A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
2.	Creator	Author's name, affiliation, country	Romain Abraham; MAPMO, Université d'Orléans; France
2.	Creator	Author's name, affiliation, country	Jean-François Delmas; CERMICS, École des Ponts Paristech; France
2.	Creator	Author's name, affiliation, country	Patrick Hoscheit; CERMICS, École des Ponts Paristech; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Gromov-Hausdorff ; Prokhorov metric ; length space ; Lévy tree ; boundedly finite measure
3.	Subject	Subject classification	60B05 ; 54E50 ; 05C80
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Agence Nationale de la Recherche
7.	Date	(YYYY-MM-DD)	2013-01-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2116
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2116
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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