# Approximation by finitely supported measures

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 2, page 343-359
- ISSN: 1292-8119

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topKloeckner, Benoît. "Approximation by finitely supported measures." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 343-359. <http://eudml.org/doc/277817>.

@article{Kloeckner2012,

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. },

author = {Kloeckner, Benoît},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Measures; Wasserstein distance; quantization; location problem; centroidal Voronoi tessellations; measures},

language = {eng},

month = {7},

number = {2},

pages = {343-359},

publisher = {EDP Sciences},

title = {Approximation by finitely supported measures},

url = {http://eudml.org/doc/277817},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Kloeckner, Benoît

TI - Approximation by finitely supported measures

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/7//

PB - EDP Sciences

VL - 18

IS - 2

SP - 343

EP - 359

AB - 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.

LA - eng

KW - Measures; Wasserstein distance; quantization; location problem; centroidal Voronoi tessellations; measures

UR - http://eudml.org/doc/277817

ER -

## References

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