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 thesum 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.
- Liouville's Boundedness Theorem
- Liouville's Conformality Theorem
- Liouville's Conic Theorem
- Liouville's Constant
- Liouville's Elliptic Function Theorem
- Liouville Space
- Liouville's Phase Space Theorem
- Liouville's Rational Approximation Theorem
- Liouville's Sphere-Preserving Theorem
- Lipschitz Condition
- Lipschitz Function
- Lipschitz's Integral
- Lissajous Curve
- Lissajous Figure
- List
- Lituus
- Lituus Inverse Curve
- LLL Algorithm
- Ln
- Lobachevsky-Bolyai-Gauss Geometry
- Lobachevsky's Formula
- Lobatto Quadrature
- Lobster
- Local Cell
- Local Degree