  We study the dual formulation of the Monge-Kantorovich optimal transportation
problem, in particular under what circumstances it is permitted in an infinite
dimensional setting to use cylindrical functions, i.e. functions of the form
$\varphi\circ P$ where $P$ is a finite-rank operator and $\varphi$ is a smooth,
compactly supported function. In the last section, some examples of
applications are presented.
