Approximations by Darboux functions in the Baire one class (Q2843898)
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scientific article; zbMATH DE number 6201666
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximations by Darboux functions in the Baire one class |
scientific article; zbMATH DE number 6201666 |
Statements
26 August 2013
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Baire one functions
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Darboux property
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0.9101372
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0.90570337
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0.9007293
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0.89944506
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0.89879465
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0.8902819
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0.8844215
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Approximations by Darboux functions in the Baire one class (English)
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In the paper, the authors using a modification of Zahorski's idea of a certain system of associated sets, show some approximations of Baire one functions by Darboux Baire one functions.NEWLINENEWLINEThe main result is the following theorem. Let \(f\:[0,1]\to \mathbb R\) be a Baire one function and let \(E\) be a Borel set bilaterally \(c\)-dense in the set of discontinuity points of \(f\). Then, there exists a Darboux Baire one function \(g\:[0,1]\to \mathbb R\) such that \(\bigl \{x\: f(x)\neq g(x)\bigr \}\subset E\).
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