Date of Original Version
This is the accepted version of the article which has been published in final form at http://dx.doi.org/10.4153/CJM-2014-044-6
Abstract or Description
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the ∞-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.
Canadian Journal of Mathematics, 67, 1358-1383.