In this short note, we show that every convex, order-bounded above functional on a Fréchet lattice is automatically continuous. This improves a result in Ruszczyński and Shapiro ((2006) Mathematics of Operations Research 31(3), 433-452.) and applies to many deviation and variability measures....

In the paradigm of von Neumann and Morgenstern (1947), a representation of affine preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we...