# Positive definite metric spaces

@article{Meckes2010PositiveDM,
title={Positive definite metric spaces},
author={Mark W. Meckes},
journal={Positivity},
year={2010},
volume={17},
pages={733-757}
}
• M. Meckes
• Published 29 December 2010
• Mathematics
• Positivity
Magnitude is a numerical invariant of finite metric spaces, recently introduced by Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended to infinite metric spaces in several a priori distinct ways. This paper develops the theory of a class of metric spaces, positive definite metric spaces, for which magnitude is more tractable than in general. Positive definiteness is a generalization of the…
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The notion of the magnitude of a compact metric space was considered in arXiv:0908.1582 with Tom Leinster, where the magnitude was calculated for line segments, circles and Cantor sets. In this paper
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Magnitude is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of
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