Construction of non-subadditive measures and discretization of Borel measures

The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that "discretization" of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures $μ_n$, each of which only takes a finite set of values, and such that $μ_n$ converges to λ in the w*-topology.