Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE's which correspond to the projection of the Benjamin-Ono equation, posed on the circle, on the first N>>1 modes in the trigonometric bases.