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In this paper, we prove the continuity of the flow of KdV on spaces ofprobability measures with respect to a combination of Wasserstein distances on$H^s$, $s>0$ and $L^2$. We are motivated by the existence of an invariantmeasure belonging to the spaces onto which these distances are defined.

Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure