  We start by first using change of measure to prove the transfer of uniqueness
in law among pairs of parabolic SPDEs differing only by a drift function, under
an almost sure $L^2$ condition on the drift/diffusion ratio. This is a
considerably weaker condition than the usual Novikov one, and it allows us to
prove uniqueness in law for the Allen-Cahn SPDE driven by space-time white
noise with diffusion function $a(t,x,u)=Cu^\gamma$, $1/2\le\gamma\le1$ and
$C\ne0$. The same transfer result is also valid for ordinary SDEs and
hyperbolic SPDEs.
