  The class of generic structures among those consisting of the measure algebra
of a probability space equipped with an automorphism is axiomatizable by
positive sentences interpreted using an approximate semantics. The separable
generic structures of this kind are exactly the ones isomorphic to the measure
algebra of a standard Lebesgue space equipped with an aperiodic
measure-preserving automorphism. The corresponding theory is complete and has
quantifier elimination; moreover it is stable with built-in canonical bases. We
give an intrinsic characterization of its independence relation.
