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\(\mathcal{D}\)-measurability and \(t\)-Wright convex functions. (English) Zbl 1334.26023
Summary: In the paper we will prove that each \(t\)-Wright convex function, which is bounded on a \(\mathcal{D}\)-measurable non-Haar meager set is continuous. Our paper refers to papers [A. Olbryś, Acta Math. Hung. 141, No. 1–2, 68–77 (2013; Zbl 1313.26017); the author, J. Math. Anal. Appl. 421, No. 2, 1479–1486 (2015; Zbl 1304.54054)] and a problem posed by K. Baron and R. Ger.

MSC:
26A51 Convexity of real functions in one variable, generalizations
39B62 Functional inequalities, including subadditivity, convexity, etc.
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