On Mauldin's classification of real functions (Q2702805)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Mauldin's classification of real functions |
scientific article |
Statements
13 March 2001
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continuity
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quasicontinuity
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Darboux function
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Baire system
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Mauldin's classification
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On Mauldin's classification of real functions (English)
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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 \(\alpha_n < \alpha \), \(n = 1, 2,\dots \)\ .
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