Spread: A Measure of the Size of Metric Spaces
2015 ◽
Vol 25
(03)
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pp. 207-225
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Keyword(s):
Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster’s magnitude of a metric space. Spread is generalized to infinite metric spaces equipped with a measure and is calculated for spheres and straight lines. For Riemannian manifolds the spread is related to the volume and total scalar curvature. A notion of scale-dependent dimension is introduced and seen for approximations to certain fractals to be numerically close to the Minkowski dimension of the original fractals.
2002 ◽
Vol 04
(04)
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pp. 725-750
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Keyword(s):
2019 ◽
Vol 72
(3)
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pp. 774-804
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Keyword(s):
2009 ◽
Vol 20
(02)
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pp. 313-329
2013 ◽
Vol 56
(3)
◽
pp. 519-535
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2013 ◽
Vol 65
(1)
◽
pp. 222-240
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Keyword(s):
2009 ◽
Vol 51
(2)
◽
pp. 301-314
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Keyword(s):
Keyword(s):
2009 ◽
Vol 80
(3)
◽
pp. 486-497
◽
2018 ◽
Vol 61
(1)
◽
pp. 33-47
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Keyword(s):
2019 ◽
Vol 20
(5)
◽
pp. 1035-1133