information:filtering, quality:corruption
Geometric mean of a continuous function

If f: → (0, ∞) {\displaystyle f:\to (0,\infty)} is a positive continuous real-valued function, its geometric mean over this interval is

For instance, taking the identity function f (x) = x {\displaystyle f(x)=x} over the unit interval shows that the geometric mean of the positive numbers between 0 and 1 is equal to 1 e {\displaystyle {\frac {1}{e}}}.