Strońska, Ewa On Mauldin’s classification of real functions. (English) Zbl 0961.26002 Math. Slovaca 49, No. 3, 287-293 (1999). The paper studies the Baire system generated by the family of all Darboux quasicontinuous, almost everywhere continuous functions. It is shown that this system of functions coincides with the family of all functions \(f\) of Mauldin’s class 1, for which the set \(C(f)\) of its continuity points is dense. It is also proved that every function \(f\) of Mauldin’s class \(\alpha > 1\) is the limit of a sequence of Darboux functions \(f_n\) of Mauldin’s class \(\alpha_n < \alpha \), \(n = 1, 2,\dots \). Reviewer: L’ubica Holá (Bratislava) MSC: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A21 Classification of real functions; Baire classification of sets and functions Keywords:continuity; quasicontinuity; Darboux function; Baire system; Mauldin’s classification PDF BibTeX XML Cite \textit{E. Strońska}, Math. Slovaca 49, No. 3, 287--293 (1999; Zbl 0961.26002) Full Text: EuDML References: [1] BRUCKNER A. M.: Differentiation of Real Functions. Lecture Notes in Math. 659, Springer-Verlag, Berlin, 1978. · Zbl 0382.26002 [2] GRANDE Z.: On the Darboux property of the sum of cliquish functions. Real Anal. Exchange 17 (1991-1992), 571-576. · Zbl 0762.26001 [3] GRANDE Z.-SOLTYSIK L.: On sequences of real functions with the Darboux property. Math. Slovaca 40 (1990), 261-265. · Zbl 0754.26001 [4] GRANDE Z.-SOLTYSIK L.: Some remarks on quasicontinuous real functions. Problemu Mat. 10 (1990), 79-86. [5] KEMPISTY S.: Sur les fonctions quasicontinuous. Fund. Math. 19 (1932), 184-197. · Zbl 0005.19802 [6] MAULDIN R. D.: The Baire order of the function continuous almost everywhere. Proc. Amer. Math. Soc. 41 (1973), 535-540. · Zbl 0274.26002 [7] PU H. W.-PU H. H.: On representation of Baire functions in a given family as sums of Baire Darboux functions with a common summand. Časopis Pěst. Mat. 112 (1987), 320-326. · Zbl 0646.26004 [8] SIERPIŃSKI W.: Sur une propriété des ensembles \(F_\sigma\) linéaires. Fund. Math. 14 (1929), 216-220. · JFM 55.0659.02 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.