New non degenerate invariant measures for the Benjamin-Ono equation (Q6195155)

A new construction of the invariant measure associated with the infinite dimensional dynamical system associated with the Benjamin-Ono equation \[ \partial_t u=H\partial_x^2 u-\partial_x(u^2) \] is proposed as a consequence of results in a recent work by \textit{P. Gérard} et al. [Acta Math. 231, No. 1, 31--88 (2023; Zbl 07779089)].