  We study the mean field equation derived by Neri in the context of the
statistical mechanics description of 2D-turbulence, under a "stochastic"
assumption on the vortex circulations. The corresponding mathematical problem
is a nonlocal semilinear elliptic equation with exponential type nonlinearity,
containing a probability measure $\mathcal P\in\mathcal M([-1,1])$ which
describes the distribution of the vortex circulations. Unlike the more
investigated "deterministic" version, we prove that Neri's equation may be
viewed as a perturbation of the widely analyzed standard mean field equation,
obtained by taking $\mathcal P=\delta_1$. In particular, in the physically
relevant case where $\mathcal P$ is non-negatively supported and $\mathcal
P(\{1\})>0$, we prove the mass quantization for blow-up sequences. We apply
this result to construct minimax type solutions on bounded domains in $\mathbb
R^2$ and on compact 2-manifolds without boundary.
