  It is widely known that when $X$ is compact Hausdorff, and when $T: X \to X$
and $f: X \to \mathbb{R}$ are continuous, \begin{equation*} P(T,f) =
\sup_{\text{$\mu$: Radon probability}} \left( h_\mu(T) + \int f\, \mathrm{d}\mu
\right), \end{equation*} where $P(T,f)$ is the "topological pressure" and
$h_\mu(T)$ is the measure theoretic entropy of $T$ with respect to $\mu$. This
result is known as "variational principle". We generalize the concept of
"topological pressure" for the case where $X$ is a separable locally compact
metric space. Our definitions are quite similar to those used in the compact
case. Our main result is the validity of the "variational principle".
