  In this paper, we study the large deviation principle of invariant measures
of stochastic reaction-diffusion lattice systems driven by multiplicative
noise. We first show that any limit of a sequence of invariant measures of the
stochastic system must be an invariant measure of the deterministic limiting
system as noise intensity approaches zero. We then prove the uniform
Freidlin-Wentzell large deviations of solution paths over all initial data and
the uniform Dembo-Zeitouni large deviations of solution paths over a compact
set of initial data. We finally establish the large deviations of invariant
measures by combining the idea of tail-ends estimates and the argument of
weighted spaces.
