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
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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
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