On the property \(N^{- 1}\) (Q1669198)
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scientific article; zbMATH DE number 6929339
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the property \(N^{- 1}\) |
scientific article; zbMATH DE number 6929339 |
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On the property \(N^{- 1}\) (English)
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30 August 2018
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Summary: We construct a continuous function \(f : [0,1] \rightarrow \mathbb{R}\) such that \(f\) possesses \(N^{- 1}\)-property, but \(f\) does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach's Theorem concerning differentiability of continuous functions with Lusin's property \((N)\) does not hold for \(N^{- 1}\)-property. Some relevant properties are presented.
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