On the rate of convergence of empirical measures in ∞-transportation distance

@inproceedings{Trillos2015OnTR,
  title={On the rate of convergence of empirical measures in ∞-transportation distance},
  author={Nicol{\'a}s Garc{\'i}a Trillos},
  year={2015}
}
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. 

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