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Christensen zero sets and measurable convex functions

Authors: Pal Fischer and Zbigniew Słodkowski
Journal: Proc. Amer. Math. Soc. 79 (1980), 449-453
MSC: Primary 28C10; Secondary 39C05, 46A99
MathSciNet review: 567990
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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 [Enhancements On Off] (What's this?)

  • [1] G. Choquet, Lectures on analysis, vol. 1, Benjamin, New York, 1969.
  • [2] J. P. R. Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255-260. MR 0326293 (48:4637)
  • [3] -, Topology and Borel structure, North-Holland, Amsterdam; American Elsevier, New York, 1974. MR 0348724 (50:1221)
  • [4] L. Schwartz, Sur le théorème du graphe fermé, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), 602-605. MR 0206676 (34:6494)
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Keywords: Haar zero set, universally measurable set, convex functions
Article copyright: © Copyright 1980 American Mathematical Society

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