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Jensen convex functions bounded above on nonzero Christensen measurable sets. (English) Zbl 1229.28027
Summary: We prove that every Jensen convex function mapping a real linear Polish space into $$\mathbb R$$ bounded above on a nonzero Christensen measurable set is convex.

##### MSC:
 28E05 Nonstandard measure theory 39B52 Functional equations for functions with more general domains and/or ranges
##### Keywords:
Christensen measurability; Jensen convex function