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A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces
- Source :
- Electronic Journal of Probability 18 (2013) 14
- Publication Year :
- 2012
-
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 L\'evy trees, which are (possibly unbounded) random real trees endowed with a locally finite measure.
- Subjects :
- Mathematics - Metric Geometry
Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Journal :
- Electronic Journal of Probability 18 (2013) 14
- Publication Type :
- Report
- Accession number :
- edsarx.1202.5464
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/EJP.v18-2116