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quasi-continuous function; cliquish function; Lebesgue function
Given a finite family of cliquish functions, $\A$, we can find a Lebesgue function $\alpha$ such that $f+ \alpha$ is Darboux and quasi-continuous for every $f \in\A$. This theorem is a generalization both of the theorem by H. W. Pu & H. H. Pu and of the theorem by Z. Grande.
[1] Z. Grande: On the Darboux property of the sum of cliquish functions. Real Anal. Exchange 17 (1991-92), no. 2, 571-576. DOI 10.2307/44153750 | MR 1171398
[2] A. Maliszewski: Sums and products of quasi-continuous functions. Real Anal. Exchange. To appear. MR 1377543 | Zbl 0843.54019
[3] H. W. Pu, H. H. Pu: On representations of Baire functions in a given family as sums of Baire Darboux functions with a common summand. Časopis Pěst. Mat. 112 (1987), no. 3, 320-326. MR 0905979 | Zbl 0646.26004
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