  Determining functionals are tools to describe the finite dimensional
long-term dynamics of infinite dimensional dynamical systems. There also exist
several applications to infinite dimensional {\em random} dynamical systems. In
these applications the convergence condition of the trajectories of an infinite
dimensional random dynamical system with respect to a finite set of linear
functionals is assumed to be either in mean or exponential with respect to the
convergence almost surely. In contrast to these ideas we introduce a
convergence concept which is based on the convergence in probability. By this
ansatz we get rid of the assumption of exponential convergence. In addition,
setting the random terms to zero we obtain usual deterministic results. We
apply our results to the 2D Navier - Stokes equations forced by a white noise.
