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On the integration of discontinuous functions. (English) JFM 07.0247.01
Der Herr Verfasser bezweckt, in dieser Note eine schärfere Fassung und einen strengeren Beweis des von Riemann in seiner Arbeit: “Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe” (Gött. Abh. XIII. p. 87, s. F. d. M. I. p. 131, JFM 01.0131.03) aufgestellten Theoremes zu geben, wonach entschieden wird, ob eine Function f(x), welche zwischen endlichen Grenzen a und b discontinuirlich aber nicht unendlich ist, eine Integration innerhalb dieser Grenzen zulässt oder nicht; wenn die Variable x sowohl, wie die Grenzen a und b reell vorausgesetzt werden.

MSC:
26A06One-variable calculus
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)