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

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 locally 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 locally finite measure.
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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.14. 〈10.1214/EJP.v18-2116〉
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Contributeur : Patrick Hoscheit <>
Soumis le : vendredi 24 février 2012 - 15:14:21
Dernière modification le : vendredi 4 mai 2018 - 01:17:28
Document(s) archivé(s) le : vendredi 25 mai 2012 - 02:26:03

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Romain Abraham, Jean-François Delmas, Patrick Hoscheit. A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.14. 〈10.1214/EJP.v18-2116〉. 〈hal-00673921〉

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