On the boundedness, Christensen measurability and continuity of \(t\)-Wright convex functions (Q485539)

The main goal of this paper is the investigation of regularity properties of \(t\)-Wright convex functions. The main theorem of the first section is a Bernstein-Doetsch type one concerning \(t\)-Wright convex functions. It states that local boundedness at point of a \(t\)-Wright convex function entails its continuity at the same point. As consequences of this theorem, similar regularity theorems are stated, when the local boundedness condition is replaced for boundedness on a set is of second category, or boundedness on a set is of positive Lebesgue measure. In the second section similar theorems are stated as in the first one using Christensen measurability.