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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a theorem concerning Baire functions
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by C. T. Tucker PDF
Proc. Amer. Math. Soc. 41 (1973), 173-178 Request permission

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
    S. Kempisty, Sur l’approximation de fonctions de première classe, Fund. Math. 2 (1921), 131-135. S. Mazurkiewicz, Sur les fonctions de classe 1, Fund. Math. 2 (1921), 28-36. W. Sierpiński, Demonstration d’un théorème sur les fonctions de première classe, Fund. Math. 2 (1921), 37-40.
  • A. C. Zaanen, Stability of order convergence and regularity in Riesz spaces, Studia Math. 31 (1968), 159–172. MR 240597, DOI 10.4064/sm-31-2-159-172
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 41 (1973), 173-178
  • MSC: Primary 46A40; Secondary 26A21
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0318834-4
  • MathSciNet review: 0318834