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The paper is devoted to studying the image of probability measures on aHilbert space under finite-dimensional analytic maps. We establish sufficientconditions under which the image of a measure has a density with respect to theLebesgue measure and continuously depends on the map. The results obtained areapplied to the 2D Navier--Stokes equations perturbed by various random forcesof low dimension.Comment: 24 page

On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier–Stokes equations