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The magnitude of a metric space: from category theory to geometric measure theory

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arxiv 1606.00095 v2 pith:H7EUGMJR submitted 2016-06-01 math.MG math.CT

Tom Leinster , Mark W. Meckes This is my paper · ORCID
classification math.MGmath.CT
keywords magnitudetheorygeometricmetricmeasurespacesanalogyarises
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Magnitude is a numerical isometric invariant of metric spaces, whose definition arises from a precise analogy between categories and metric spaces. Despite this exotic provenance, magnitude turns out to encode many invariants from integral geometry and geometric measure theory, including volume, capacity, dimension, and intrinsic volumes. This paper will give an overview of the theory of magnitude, from its category-theoretic genesis to its connections with these geometric quantities.

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  1. Approximating the Convex Hull via Metric Space Magnitude

    math.AT 2019-08 conditional novelty 6.0 of 10

    A new point score, the moment, derived from metric space magnitude, allows approximating a data set's convex hull by keeping only high-moment points.

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