On fragmented convex functions (Q2287350)

Let \(X\) be a compact convex set and let \(\text{Ext}(X)\) be its set of extreme points. An interesting take-off from the continuous convex/affine function theory is to see to what extent one can relax the continuity assumption. It is well known that Baire class 1 functions will very often do. This interesting paper deals with these problems for convex functions satisfying the point of continuity property. For such an \(f\), \(f \leq 0\) on \(\text{Ext}(X)\) implies \(f \leq 0\) on \(X\). A class of such functions also respects the Choquet ordering on non-negative measures on~\(X\).