Before revision:  We apply these results by proving tight complexity bounds, with respect to identifiable properties , for variance, financial risk measures, entropy, norms, and new properties of interest. We then show how some of these bounds can extend to other practical classes of properties, and conclude with a discussion of open directions.
After revision:  We apply these results by proving tight complexity bounds, with respect to identifiable properties , for variance, financial risk measures, entropy, norms, and several classes of financial risk measures. We conclude with discussion and open directions.