  We provide a necessary and sufficient condition under which a convex set is
approachable in a game with partial monitoring, i.e.\ where players do not
observe their opponents' moves but receive random signals. This condition is an
extension of Blackwell's Criterion in the full monitoring framework, where
players observe at least their payoffs. When our condition is fulfilled, we
construct explicitly an approachability strategy, derived from a strategy
satisfying some internal consistency property in an auxiliary game. We also
provide an example of a convex set, that is neither (weakly)-approachable nor
(weakly)-excludable, a situation that cannot occur in the full monitoring case.
We finally apply our result to describe an $\epsilon$-optimal strategy of the
uninformed player in a zero-sum repeated game with incomplete information on
one side.
