Continuity of convex functions
In this paper, we consider the set V(K) of all convex real-valued functions defined on convex compacts Kс M n and find conditions under which all functions fe V(K) are scattered continuous. It is shown that there exist functions fe V(K) that are not Borel, and, for any ordinal а1, there are functions fe V(K) that exactly belong to the а th Baire class.