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A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces
- Source :
- Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.14. ⟨10.1214/EJP.v18-2116⟩
- Publication Year :
- 2013
- Publisher :
- HAL CCSD, 2013.
-
Abstract
- International audience; 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.
- Subjects :
- Probability (math.PR)
boundedly finite measure
Metric Geometry (math.MG)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Mathematics - Metric Geometry
51F99, 05C05, 05C80, 60D05
FOS: Mathematics
Gromov-Hausdorff
Levy tree
Mathematics::Metric Geometry
Prokhorov metric
[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
Mathematics - Probability
length space
Subjects
Details
- Language :
- English
- ISSN :
- 10836489
- Database :
- OpenAIRE
- Journal :
- Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.14. ⟨10.1214/EJP.v18-2116⟩
- Accession number :
- edsair.doi.dedup.....2ee5e006791e0df2079bfc11a7559c47