  New transportation cost inequalities are derived by means of elementary large
deviation reasonings. Their dual characterization is proved; this provides an
extension of a well-known result of S. Bobkov and F. G\"{o}tze. Their
tensorization properties are investigated. Sufficient conditions (and necessary
conditions too) for these inequalities are stated in terms of the integrability
of the reference measure. Applying these results leads to new deviation
results: concentration of measure and deviations of empirical processes.
