  Aim of this paper is to show that it makes sense to write the continuity
equation on a metric measure space $(X,d,m)$ and that absolutely continuous
curves $\mu_t$ w.r.t. the distance $W_2$ can be completely characterized as
solutions of the continuity equation itself, provided we impose the condition
$\mu_t\leq Cm$ for every $t$ and some $C>0$.
