Ergodic quasi-invariant measures on topologically mixing subshifts are\n isomorphic to Bernoulli shifts

We prove that a shift ergodic measure on a topologically mixing sub-shift is\nisomorphic to a Bernoulli shift whenever it is quasi invariant under\npermutations of finite number of coordinates. We prove also that Gibbs measures\non topologically mixing subshift of finite type are quasi invariant.\n