If the functional measure is not translationally invariant, it might be possible to express it as the product M [ φ ] D φ, where M is a functional and D φ is a translationally invariant measure. This is true, for example, for nonlinear sigma models where the target space is diffeomorphic to R. However, if the target manifold is some topologically nontrivial space, the concept of a translation does not even make any sense.