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 <sup>n</sup> 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 а<ю <sub>1</sub>, there are functions fe V(K) that exactly belong to the а th Baire class.