Hausdorff metric structure of the space of probability measures

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Abstract

The Hausdorff distance between two bounded functions on the real line was introduced by B. Sendov and B. Penkov. On the class of distribution functions it agrees with the Levi distance. The goal of this article is to analyze the Levi-Prokhorov metric and a new metric in terms of the relation between their structure and the Hausdorff distance.

Original languageEnglish
Pages (from-to)2275-2288
Number of pages14
JournalJournal of Soviet Mathematics
Volume17
Issue number6
DOIs
StatePublished - Dec 1981

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