MOSCO APPROXIMATION OF INTEGRANDS AND INTEGRAL FUNCTIONALS

We show that given a lower semi-continuous convex integrand f, satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges to f and such that the sequence of conjugate integrand's Mosco converges to f*. Moreover this sequence can chosen so that the associated integral functionals respectively defined on L(1) (X) and L(infinity) (X*) Mosco converge too.