  Stochastic Navier--Stokes equations in a thin three-dimensional domain are
considered, driven by additive noise. The convergence of martingale solution of
the stochastic Navier--Stokes equations in a thin three-dimensional domain to
the unique martingale solution of the 2D stochastic Navier--Stokes equations,
as the thickness of the film vanishes, is established. Hence, we justify the
approximation of 3D Navier--Stokes equations driven by random forcing by its
corresponding two-dimensional setting in applications.
