Geodesic
Discrete approximation of continuous measures and some applications
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 99-110

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We study the best approximation (in the Kantorovich–Rubinshteĭn metric) of continuous measures on the straight line by measures concentrated at finitely many points. An algorithm to obtain such measures is constructed and the questions of their existence and uniqueness are considered. Applications of the results to some problems of mathematical economics are studied.
Keywords: continuous measures, point measures, best approximation, migration resistance. 
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     author = {E. O. Rapoport},
     title = {Discrete approximation of continuous measures and some applications},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a9/}
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E. O. Rapoport. Discrete approximation of continuous measures and some applications. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 99-110. http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a9/