  In this work, we show the consistency of an approach for solving robust
optimization problems using sequences of sub-problems generated by ergodic
measure preserving transformations.
  The main result of this paper is that the minimizers and the optimal value of
the sub-problems converge, in some sense, to the minimizers and the optimal
value of the initial problem, respectively. Our result particularly implies the
consistency of the scenario approach for nonconvex optimization problems.
Finally, we show that our method can also be used to solve infinite programming
problems.
