We prove an integral-representation result for limits of non-local quadratic forms on H-0(1)(Omega), with Omega a bounded open subset of R-d, extending the representation on C-c(infinity)(Omega) given by the Beurling Deny formula in the theory of Dirichletforms. We give a counter example showing that a corresponding representation may not hold if we consider analogous functionals in W-0(1,p)(Omega), with p not equal 2and 1 < p <= d
