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

Thomas Leinster; Mark W. Meckes

doi:10.1515/9783110550832-005

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

Thomas Leinster, Mark W. Meckes

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

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.

Original language	English
Title of host publication	Measure Theory in Non-Smooth Spaces
Publisher	De Gruyter Open
Pages	156-193
Number of pages	32
DOIs	https://doi.org/10.1515/9783110550832-005
Publication status	Published - 2017

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10.1515/9783110550832-005

1606.00095v2Accepted author manuscript, 403 KB

Tom Leinster
- School of Mathematics - Personal Chair of Category Theory
Person: Academic: Research Active

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

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Tom Leinster

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