  This work aims to investigate the existence of ergodic invariant measures and
its uniqueness, associated with obstacle problems governed by a T-monotone
operator defined on Sobolev spaces and driven by a multiplicative noise in a
bounded domain of $\mathbb{R}^d$. First, we verify that the solution of a
stochastic obstacle problem defines a Feller-Markov process. Then, we prove the
existence of ergodic invariant measures and its uniqueness, under suitablee
assumptions. We use \textit{"Krylov-Bogoliubov Theorem"}, where the control of
the singularities caused by the obstacle is fundamental.
