On Mauldin’s classification of real functions. (English) Zbl 0961.26002

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 \(\alpha_n < \alpha \), \(n = 1, 2,\dots \).


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
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