  We consider suitable weak solutions of 2-dimensional Euler equations on
bounded domains, and show that the class of completely random measures is
infinitesimally invariant for the dynamics. Space regularity of samples of
these random fields falls outside of the well-posedness regime of the PDE under
consideration, so it is necessary to resort to stochastic integrals with
respect to the candidate invariant measure in order to give a definition of the
dynamics. Our findings generalize and unify previous results on Gaussian
stationary solutions of Euler equations and point vortex dynamics. We also
discuss difficulties arising when attempting to produce a solution flow for
Euler's equations preserving independently scattered random measures.
