Condition for Darboux Integrability/Historical Note

Historical Note on Condition for Darboux Integrability

The necessary and sufficient conditions for the existence of a Riemann integral were determined by Riemann in his paper Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe of $1854$, on the subject of Fourier series.

It is noted that the proof given on this page refers specifically to the Darboux integral, which is a simpler but equivalent concept to that introduced by Riemann.

That they are equivalent is given in Equivalence of Definitions of Riemann and Darboux Integrals

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.32$: Riemann ($\text {1826}$ – $\text {1866}$)