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

   
@article{EJP2116,
	author = {Romain Abraham and Jean-François Delmas and Patrick Hoscheit},
	title = {A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {18},
	year = {2013},
	keywords = {Gromov-Hausdorff ; Prokhorov metric ; length space ; Lévy tree ; boundedly finite measure},
	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.},
	pages = {no. 14, 1-21},
	issn = {1083-6489},
	doi = {10.1214/EJP.v18-2116},    
        url = {http://ejp.ejpecp.org/article/view/2116}}