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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a theorem concerning Baire functions


Author: C. T. Tucker
Journal: Proc. Amer. Math. Soc. 41 (1973), 173-178
MSC: Primary 46A40; Secondary 26A21
MathSciNet review: 0318834
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Abstract: Mazurkiewicz, Sierpiński, and Kempisty proved that a function in Baire class 1 is the uniform limit of a sequence of functions each of which is the difference of two upper semicontinuous functions. A generalization of this theorem is shown to be a consequence of order and linear properties alone.


References [Enhancements On Off] (What's this?)

  • [1] S. Kempisty, Sur l'approximation de fonctions de première classe, Fund. Math. 2 (1921), 131-135.
  • [2] S. Mazurkiewicz, Sur les fonctions de classe 1, Fund. Math. 2 (1921), 28-36.
  • [3] W. Sierpiński, Demonstration d'un théorème sur les fonctions de première classe, Fund. Math. 2 (1921), 37-40.
  • [4] A. C. Zaanen, Stability of order convergence and regularity in Riesz spaces, Studia Math. 31 (1968), 159–172. MR 0240597 (39 #1944)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0318834-4
PII: S 0002-9939(1973)0318834-4
Keywords: Baire functions, Riesz space, order convergence, relative uniform convergence
Article copyright: © Copyright 1973 American Mathematical Society