| Título: | A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces |
| Autores: |
Abraham, Romain; MAPMO, Université d'Orléans Delmas, Jean-François; CERMICS, École des Ponts Paristech Hoscheit, Patrick; CERMICS, École des Ponts Paristech |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Gromov-Hausdorff ; Prokhorov metric ; length space ; Lévy tree ; boundedly finite measure 60B05 ; 54E50 ; 05C80 |
| Descripción: | 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. |
| Idioma: | Inglés |
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