×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite