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• W2962959486 endingPage "905" @default.
• W2962959486 startingPage "857" @default.
• W2962959486 abstract "Magnitude is a real-valued invariant of metric spaces, analogous to Euler characteristic of topological spaces and cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies the analogies between cardinality- like invariants in mathematics. Although this motivation is a world away from geometric measure, magnitude, when applied to subsets of R n , turns out to be intimately related to invariants such as volume, surface area, perimeter and dimension. We describe several aspects of this relationship, providing evidence for a conjecture (first stated in joint work with Willerton) that magnitude encodes all the most important invariants of classical integral geometry." @default.
• W2962959486 created "2019-07-30" @default.
• W2962959486 creator A5047971691 @default.
• W2962959486 date "2013-01-01" @default.
• W2962959486 modified "2023-09-27" @default.
• W2962959486 title "The magnitude of metric spaces" @default.
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• W2962959486 hasPublicationYear "2013" @default.
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