Steffensen's inequality

Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen.

It is an integral inequality in real analysis, stating:
 * If ƒ : [a, b] → R is a non-negative, monotonically decreasing, integrable function
 * and g : [a, b] → [0, 1] is another integrable function, then


 * $$\int_{b - k}^{b} f(x) \, dx \leq \int_{a}^{b} f(x) g(x) \, dx \leq \int_{a}^{a + k} f(x) \, dx,$$
 * where
 * $$k = \int_{a}^{b} g(x) \, dx.$$