Definition:Ordinary Mean Value

Definition
Let $f: \N \to \C$ be an arithmetic function.

The (ordinary) mean value of $f$ is the limit:
 * $M \left({f}\right) = \displaystyle \lim_{x \mathop \to \infty} \frac 1 x \sum_{n \mathop \le x} f \left({n}\right)$

if it exists.

Also known as
The ordinary mean value is also known as asymptotic mean value, or simply mean value.

Also see

 * Definition:Logarithmic Mean Value