We present a simple nonstandard construction of a global Euler flow and some classes of measures invariant with respect to the flow, including examples of non-Gaussian ones. We also obtain existence of statistical solutions of the Euler equation for a wide class of initial measures.
"The Euler Equation: A Uniform Nonstandard Construction of a Global Flow, Invariant Measures and Statistical Solutions." Ann. Appl. Probab. 3 (1) 212 - 227, February, 1993. https://doi.org/10.1214/aoap/1177005516