A simultaneous solution to two problems of derivatives (Q1086369)
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scientific article; zbMATH DE number 3983522
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simultaneous solution to two problems of derivatives |
scientific article; zbMATH DE number 3983522 |
Statements
A simultaneous solution to two problems of derivatives (English)
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1986
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Let \(A\) be a nonvoid countable subset of the unit interval \([0,1]\) and let \(B\) be an \(F_{\sigma}\)-subset of \([0,1]\) disjoint from \(A\). Then there exists a derivative \(f\) on \([0,1]\) such that \(0\leq f\leq 1\), \(f=0\) on \(A\), \(f>0\) on \(B\), and such that the extended real valued function \(1/f\) is also a derivative.
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Lebesgue summable functions
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knot point
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derivative f such that 1/f is also a derivative
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Dini derivatives
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