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On the averages of Darboux functions


Author: Aleksander Maliszewski
Journal: Trans. Amer. Math. Soc. 350 (1998), 2833-2846
MSC (1991): Primary 26A21, 54C30.; Secondary 26A15, 54C08
DOI: https://doi.org/10.1090/S0002-9947-98-02267-3
MathSciNet review: 1617344
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Abstract: Let $\mathbf{A} $ be the family of functions which can be written as the average of two comparable Darboux functions. In 1974 A. M. Bruckner, J. G. Ceder, and T. L. Pearson characterized the family $\mathbf{A} $ and showed that if $\alpha \ge 2$, then $\mathbf{A} \cap {\mathbf B}_\alpha$ is the family of the averages of comparable Darboux functions in Baire class $\alpha$. They also asked whether the latter result holds true also for $\alpha =1$. The main goal of this paper is to answer this question in the negative and to characterize the family of the averages of comparable Darboux Baire one functions.


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Additional Information

Aleksander Maliszewski
Affiliation: Department of Mathematics, Pedagogical University, pl. Weyssenhoffa 11, 85-042 Bydgoszcz, Poland
Email: amal@wsp.bydgoszcz.pl

DOI: https://doi.org/10.1090/S0002-9947-98-02267-3
Keywords: Darboux function, comparable functions, average of functions
Received by editor(s): July 30, 1996
Additional Notes: Partially supported by NSF Cooperative Research Grant INT-9600548, with its Polish part being financed by the Polish Academy of Sciences
Article copyright: © Copyright 1998 American Mathematical Society

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