  Existence of distributional solutions of a modified Surface Quasi-Geostrophic
equation (mSQG) is proven for $\mu$-almost every initial condition, where $\mu$
is a suitable Gaussian measure. The result is the by-product of existence of a
stationary solution with white noise marginal. This solution is constructed as
a limit of random point vortices, uniformly distributed and rescaled according
to the Central Limit Theorem.
