Magnitude, Diversity, Capacities, and Dimensions of Metric Spaces

@article{Meckes2013MagnitudeDC,
  title={Magnitude, Diversity, Capacities, and Dimensions of Metric Spaces},
  author={Mark W. Meckes},
  journal={Potential Analysis},
  year={2013},
  volume={42},
  pages={549-572}
}
  • M. Meckes
  • Published 25 August 2013
  • Mathematics
  • Potential Analysis
Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural and direct manner than in previous works by Leinster, Willerton, and the author. The new definition uncovers a previously unknown relationship between magnitude and capacities of sets. Exploiting this relationship, it is shown that for a compact subset of… 
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