Mosco approximation of integrands and integral functionals

It is shown that, given a lower semicontinuous convex integrandf satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges tof and such that the sequence of conjugate integrands Mosco converges tof^*. Moreover, this sequence can be chosen so that the sequence of associated integral functionals, respectively defined onL¹(X) andL(X^*), Mosco converges as well.We wish to thank Professor Erik J. Balder for interesting remarks on the first version of this work.