A Borel probability measure is residual if it gives measure zero to all meager subsets. We first give some existence results about this class of measures. Then they are applied in order to get some non-existence results for probability measures defined on Boolean algebras. This is done on the basis of some duality methods. Finally we prove that the range of a nonatomic probability measure defined on a Boolean algebra which satisfies the c.c.c. is dense in the unit inter val.