  Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map
with the specification property, and $\varphi: X \mapsto \IR$ be a continuous
function. We prove a variational principle for topological pressure (in the
sense of Pesin and Pitskel) for non-compact sets of the form \[ \{x \in X :
\lim_{n \ra \infty} \frac{1}{n} \sum_{i = 0}^{n-1} \varphi (f^i (x)) = \alpha
\}. \] Analogous results were previously known for topological entropy. As an
application, we prove multifractal analysis results for the entropy spectrum of
a suspension flow over a continuous map with specification and the dimension
spectrum of certain non-uniformly expanding interval maps.
