Approximation pour la distance de Wasserstein

Let $\text{C}$ be a set of probability-measures and P a probability on $\text{R}{}^{\mathrm{d}}$. Under some conditions, we show that we have a solution to the approximation problem of P by $\text{C}\text{.}$ There exists a probability $\text{Q}{}_0\text{∈}\text{C}$, such that $\text{l(P,Q}{}_0\text{)?l(P,Q),}\text{?Q∈}\text{C}$ where l is the square of the Wasserstein distance. To cite this article: N. Belili, H. Heinich, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 537–540.