In the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.
This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.
