An existence theorem for higher Peano derivatives in \(R^ m\) (Q1098954)
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scientific article; zbMATH DE number 4038130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence theorem for higher Peano derivatives in \(R^ m\) |
scientific article; zbMATH DE number 4038130 |
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An existence theorem for higher Peano derivatives in \(R^ m\) (English)
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1988
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It follows from the Denjoy-Young-Saks theorem that if \(f(x+h)=f(x)+O(| h|)\) for every x then f is almost everywhere differentiable. This theorem was generalized by many authors. In this paper a new real variable proof is given of the most general version of this theorem, which can be used for higher Peano derivatives in multiple dimensional real spaces.
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Denjoy-Young-Saks theorem
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higher Peano derivatives
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