## Darboux Integral

A variant of the Riemann Integral defined when the Upper and Lower Integrals, taken as limits of the Lower Sum

and Upper Sum

are equal. Here, is a Real Function, is a monotonic increasing function with respect to which the sum is taken, denotes the lower bound of over the interval , and denotes the upper bound.

See also Lower Integral, Lower Sum, Riemann Integral, Upper Integral, Upper Sum

References

Kestelman, H. Modern Theories of Integration, 2nd rev. ed. New York: Dover, p. 250, 1960.