Christensen zero sets and measurable convex functions
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- by Pal Fischer and Zbigniew Słodkowski PDF
- Proc. Amer. Math. Soc. 79 (1980), 449-453 Request permission
Abstract:
A notion of measurability in abelian Polish groups related to Christensen’s Haar zero set is studied. It is shown that a measurable homomorphism or a measurable Jensen convex function defined on a real linear Polish space is continuous.References
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G. Choquet, Lectures on analysis, vol. 1, Benjamin, New York, 1969.
- Jens Peter Reus Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255–260 (1973). MR 326293, DOI 10.1007/BF02762799
- J. P. R. Christensen, Topology and Borel structure, North-Holland Mathematics Studies, Vol. 10, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Descriptive topology and set theory with applications to functional analysis and measure theory. MR 0348724
- Laurent Schwartz, Sur le théorème du graphe fermé, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A602–A605 (French). MR 206676 W. Sierpinski, Sur les fonctions convexes mesurables, Fund. Math. 1 (1920), 125-129.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 449-453
- MSC: Primary 28C10; Secondary 39C05, 46A99
- DOI: https://doi.org/10.1090/S0002-9939-1980-0567990-5
- MathSciNet review: 567990