In this paper, we prove that the integral functional F[u] : BV(;Rm) → R defined by F[u] :=  f (x, u(x),∇u(x)) dx +    1 0 f∞  x, uθ (x), dDsu d|Dsu| (x)  dθ d|Dsu|(x) is continuous over BV(;Rm), with respect to the topology of area-strict convergence, a topology in which (W1,1 ∩ C∞ )(;Rm) is dense. This provides conclusive justification for the…