  In view of the applications to the asymptotic analysis of a family of
obstacle problems, we consider a class of convex local functionals $F(u,A)$,
defined for all functions $u$ in a suitable vector valued Sobolev space and for
all open sets $A$ in ${\bf R}^n$. Sufficient conditions are given in order to
obtain an integral representation of the form $F(u,A)=\int_A f(x,u(x))\,d\mu +
\nu(A)$, where $\mu$ and $\nu$ are Borel measures and $f$ is convex in the
second variable.
