Jensen Convex Functions Bounded Above on Nonzero Christensen Measurable Sets

• Autorzy: Eliza Jabłońska
• Języki publikacji: EN

Abstrakty

EN

We prove that every Jensen convex function mapping a real linear Polish space into R bounded above on a nonzero Christensen measurable set is convex.(original abstract)

Słowa kluczowe

EN

Mathematics; Functions; Mathematical functions

PL

Matematyka; Funkcje; Funkcje matematyczne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2009
• Tom: 23
• Strony: 53--55

Twórcy

autor

Eliza Jabłońska

• Rzeszów University of Technology

Bibliografia

• Brzdęk J., The Christensen measurable solutions of a generalization of the Gołab- Schinzel functional equation, Ann. Polon. Math. 64 (1996), no. 3, 195-205.
• Christensen J.P.R., On sets ofHaar measure zero in abelian Polish groups. Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972), Israel J. Math. 13 (1972), 255-260.
• Christensen J.P.R., Topology and Borel structure. Descriptive topology and set theory with applications to functional analysis and measure theory. North-Holland Mathematics Studies, Vol. 10. (Notas de Matematica, No. 51). North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974.
• Fischer P., Słodkowski Z., Christensen zero sets and measurable convex functions, Proc. Amer. Math. Soc. 79 (1980), no. 3, 449-453.
• Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality. Second edition, Birkhauser Verlag AG, Basel-Boston-Berlin, 2009.
• Report of Meeting, The Twenty-first International Symposium on Functional Equations, August 6 - August 13, 1983, Konolfingen, Switzerland, Aequationes Math. 26 (1984), 225-294.