Integrability conditions for approximate derivatives (Q1073935)
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scientific article; zbMATH DE number 3946502
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integrability conditions for approximate derivatives |
scientific article; zbMATH DE number 3946502 |
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Integrability conditions for approximate derivatives (English)
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1985
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Let F be a real function on [0,1]. Let \(F^*\) equal F' wherever it exists and 0 elsewhere. Let F be approximately differentiable. Then \(F^*\) is Denjoy integrable in the restricted sense if and only if \(F'_{ap}\) is integrable in the same sense. Two counterexamples show that the wide Denjoy integral cannot replace the restricted one in the above theorem.
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approximate derivatives
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Denjoy integral
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