\begin{definition}[Definition:Dirichlet Density]
Let $\PP$ be a set of prime numbers.
For $s \in \C$, let $\ds \map f s = \sum_{p \mathop \in \PP}: p^{-s}$.
$S$ has '''Dirichlet density''' $\alpha$ {{iff}}:
:$\ds \lim_{s \mathop \to 1^+} \set {\frac {\map f s} {\map \ln {s - 1} } } = -\alpha$
where $1^+$ indicates a limit from above along the real line.
{{NamedforDef|Johann Peter Gustav Lejeune Dirichlet|cat = Dirichlet}}
Category:Definitions/Analytic Number Theory
\end{definition}