Approximation of capacities with additive measures

For a space of non-additive regular measures on a metric compactum with the Prokhorov-style metric, it is shown that the problem of approximation of arbitrary measure with an additive measure on a fixed finite subspace reduces to linear optimization problem with parameters dependent on the values of the measure on a finite number of sets. An algorithm for such an approximation, which is more efficient than the straighforward usage of simplex method, is presented.