\begin{definition}[Definition:Logarithmic Mean Value]
Let $f: \N \to \C$ be an arithmetic function.
The '''logarithmic mean value''' of $f$ is the limit:
:$\map L f = \ds \lim_{x \mathop \to \infty} \frac 1 {\ln x} \sum_{n \mathop \le x} \frac {\map f n} n$
if it exists.
\end{definition}