  The optimal mass transportation was introduced by Monge some 200 years ago
and is, today, the source of large number of results in analysis, geometry and
convexity. Here I investigate a new, surprising link between optimal
transformations obtained by different Lagrangian actions on Riemannian
manifolds. As a special case, for any pair of non-negative measures
$\lambda^+,\lambda^-$ of equal mass $$ W_1(\lambda^-, \lambda^+)= \lim_{\eps\to
0} \eps^{-1}\inf_{\mu} W_p(\mu+\eps\lambda^-, \mu+\eps\lambda^+)$$ where $W_p$,
$p\geq 1$ is the Wasserstein distance and the infimum is over the set of
probability measures in the ambient space.
