A variational integral for Banach-valued functions (Q5932452)
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scientific article; zbMATH DE number 1602858
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A variational integral for Banach-valued functions |
scientific article; zbMATH DE number 1602858 |
Statements
A variational integral for Banach-valued functions (English)
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10 June 2001
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It is shown that for a Banach space \(X\) valued function the Henstock variational integral is equivalent to the Kurzweil-Henstock integral if and only if \(X\) is finite-dimensional. The main argument uses the fact that the classical form of the Saks-Henstock lemma fails in some infinite-dimensional Banach spaces.
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variational integral
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Kurzweil-Henstock integral
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Banach space-valued function
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