  A linear stochastic transport equation with non-regular coefficients is
considered. Under the same assumption of the deterministic theory, all weak
$L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate,
uniqueness of weak $L^\infty$-solutions does not require essential new
assumptions, opposite to the deterministic case where for instance the
divergence of the drift is asked to be bounded. The proof gives a new
explanation why bilinear multiplicative noise may have a regularizing effect.
