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Approximation by finitely supported measures

Published online by Cambridge University Press:  13 April 2011

Benoît Kloeckner
Benoît Kloeckner*
Affiliation:
Institut Fourier, Université Joseph Fourier, BP 53, 38041 Grenoble, France. Benoit.Kloeckner@ujf-grenoble.fr
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Abstract

We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.

Keywords

MeasuresWasserstein distancequantizationlocation problemcentroidal Voronoi tessellations
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 2 , April 2012 , pp. 343 - 359
Copyright
© EDP Sciences, SMAI, 2011

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