Functions with a \({\mathcal D}_*\)-integrable symmetric derivative (Q1080544)
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scientific article; zbMATH DE number 3966523
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Functions with a \({\mathcal D}_*\)-integrable symmetric derivative |
scientific article; zbMATH DE number 3966523 |
Statements
Functions with a \({\mathcal D}_*\)-integrable symmetric derivative (English)
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1986
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Let a function \(f: [a,b]\to R\) be symmetrically differentiable at every point and let its symmetric derivative \(f_ s'\) be integrable in the Denjoy-Perron sense. Then there exists a function \(M: [a,b]\to R\) of the class \(ACG_*\) such that the set \(\{x: f(x)\neq M(x)\}\) contains no subset which is non-empty and dense in itself.
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function whose symmetric derivative is Denjoy-Perron integrable
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\(ACG_ *\)-function
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