A magnitude for metric measure spaces is defined using geodesic integrals; it recovers finite-space magnitude (rescaled) and manifold volume in special cases, and appears sensitive to geodesic non-uniqueness.
Mumford,An Easy Case of Feynman’s Path Integrals, 2014.https://www.dam.brown.edu/people/ mumford/blog/BookPosts/14c-Feynman.pdf.↑5
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Magnitude of metric measure spaces and integrals over geodesics
A magnitude for metric measure spaces is defined using geodesic integrals; it recovers finite-space magnitude (rescaled) and manifold volume in special cases, and appears sensitive to geodesic non-uniqueness.