  The aim of this note is to show that Alexandrov solutions of the Monge-Ampere
equation, with right hand side bounded away from zero and infinity, converge
strongly in $W^{2,1}_{loc}$ if their right hand side converge strongly in
$L^1_{loc}$. As a corollary we deduce strong $W^{1,1}_{loc}$ stability of
optimal transport maps.
