  We consider Glauber-type stochastic dynamics of continuous systems
\cite{BCC02}, \cite{KL03}, a particular case of spatial birth-and-death
processes. The dynamics is defined by a Markov generator in such a way that
Gibbs measures of Ruelle type are symmetrizing, and hence invariant for the
stochastic dynamics. In this work we show that the converse statement is also
true. Namely, all invariant measures satisfying Ruelle bound condition are
grand canonical Gibbsian for the potential defining the dynamics. The proof is
based on the observation that the well-known Kirkwood-Salsburg equation for
correlation functions is indeed an equilibrium equation for the stochastic
dynamics.
