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math.MG2025
Is magnitude 'generically continuous' for finite metric spaces?
Hirokazu Katsumasa, Emily Roff, Masahiko Yoshinaga
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the m…
math.MG2019
The maximum entropy of a metric space
Tom Leinster, Emily Roff
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with…