On integration in quasi-Banach spaces of sequences (Q2793890)
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scientific article; zbMATH DE number 6557665
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On integration in quasi-Banach spaces of sequences |
scientific article; zbMATH DE number 6557665 |
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17 March 2016
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quasi-Banach spaces
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quasi-Sobolev spaces
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analytic vector-function
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Riemann integral
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0.9198575
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0.9180666
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0.91668344
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0.90871966
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0.9012495
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On integration in quasi-Banach spaces of sequences (English)
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It is proved in Theorem 3.5.2 of [\textit{S. Rolewicz}, Metric linear spaces. 2nd ed. Boston-Lancaster (1985; Zbl 0573.46001)] that every analytic function \(f: [a,b] \to X\) taking values in a locally pseudoconvex \(F\)-space is Riemann integrable. Here the authors quote this theorem, specialising the assumption to \(X\) being a weighted \(\ell_p\)-space, \(0<p\leq1\). Further, they mention the same consequences as in [loc.\ cit.].
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