The structures of Hausdorff metric in non-Archimedean spaces

Details The structures of Hausdorff metric in non-Archimedean spaces The structures of Hausdorff metric in non-Archimedean spaces

2011-05-09

arxiv.org/abs/1105.1605v1

Mathematics

Metric Geometry

43 pages

Scientific paper

As a counterpart to some extent of the Levy-Prohorov metric in the probability measure spaces, in this paper, we introduce and construct several ball-type metric structures $ \widehat{\beta}_{X, Y}^{\lambda} $ and $ \widehat{\beta}_{X, Y}^{\ast \lambda} $ on mappings over spaces of balls in non-Archimedean spaces. We obtain some basic facts on them. These metrics behave very differently comparing with the usual Levy-Prohorov metric, and they are interesting in themselves. The Dudley type metric in the space of non-Archimedean measures as well as several related Hausdorff metric structures in non-Archimedean spaces are also established and studied.

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