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On the boundedness, Christensen measurability and continuity of \(t\)-Wright convex functions. (English) Zbl 1313.26017
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.

26A51 Convexity of real functions in one variable, generalizations
Full Text: DOI
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