On the asymptotic magnitude of subsets of Euclidean space - Mathematics > Metric GeometryReport as inadecuate




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Abstract: Magnitude is a canonical invariant of finite metric spaces which has itsorigins in category theory; it is analogous to cardinality of finite sets.Here, by approximating certain compact subsets of Euclidean space with finitesubsets, the magnitudes of line segments, circles and Cantor sets are definedand calculated. It is observed that asymptotically these satisfy theinclusion-exclusion principle, relating them to intrinsic volumes of polyconvexsets.



Author: Tom Leinster, Simon Willerton

Source: https://arxiv.org/







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