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On the measurability and the Baire property of $$t$$-Wright-convex functions. (English) Zbl 1067.26009
The main result of the paper shows that if a real function is $$t$$-Wright-convex and either Lebesgue measurable or Baire measurable, then it has to be a continuous convex function. The result thus obtained extends the analogous statements obtained for Jensen-convexity by Bernstein and Doetsch and by Sierpiński.

##### MSC:
 26A51 Convexity of real functions in one variable, generalizations 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 39B62 Functional inequalities, including subadditivity, convexity, etc. 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
##### Keywords:
convexity; Wright convexity; regularity properties
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