On mean-value theorem in Riemann-Stieltjes' integral. (Q2596036)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On mean-value theorem in Riemann-Stieltjes' integral. |
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On mean-value theorem in Riemann-Stieltjes' integral. (English)
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1938
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Die für gewöhnliche Stieltjes-Integrale gültige Beziehung, wonach mit \(\int\limits_{a}^{b}f\,dg\) auch \(\int\limits_{a}^{b}g\,df\) existiert und die Summe dieser Integrale den Wert \(f(b)g(b)-f(a)g(a)\) hat, wird übertragen auf die modifizierten Stieltjes-Integrale von \textit{Pollard} (The Stieltjes' integral and its generalisations, Quart. J. Math. 49 (1921), 73-138 (F. d. M. 48, 1199 (JFM 48.1199.*)), insbesondere p. 94).
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