  In this paper we consider the periodic Benjemin-Ono equation. We will
establish the invariance of the Gibbs measure associated to this equation, thus
answering a question raised in Tzvetkov [20]. As an intermediate step, we also
obtain a local well-posedness result in Besov-type spaces rougher than L^2,
extending the L^2 well-posedness result of Molinet [14].
