Steffensen's inequality

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Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen. It is an integral inequality in real analysis, stating:

If ƒ : [ab] → R is a non-negative, monotonically decreasing, integrable function
and g : [ab] → [0, 1] is another integrable function, then
[math]\displaystyle{ \int_{b - k}^{b} f(x) \, dx \leq \int_{a}^{b} f(x) g(x) \, dx \leq \int_{a}^{a + k} f(x) \, dx, }[/math]
where
[math]\displaystyle{ k = \int_{a}^{b} g(x) \, dx. }[/math]

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