On linear sets in space \(C\) consisting of functions of bounded variation. (Q2587262)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On linear sets in space \(C\) consisting of functions of bounded variation. |
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On linear sets in space \(C\) consisting of functions of bounded variation. (English)
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1940
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Verf. beweist: \(E\) sei eine lineare abgeschlossene Teilmenge des Raumes \(C_{(0, 1)}\) aller stetigen Funktionen \(x (t)\) (\(0 \leqq t \leqq 1\)) mit der Norm \(\| x \| = \max\limits_{0 \leqq t \leqq 1} | x(t)|\). Besteht \(E\) nur aus Funktionen von beschränkter Schwankung, so ist die Dimension von \(E\) endlich.
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