  We prove uniqueness in law for a class of parabolic stochastic partial
differential equations in an interval driven by a functional A(u) of the
temperature u times a space-time white noise. The functional A(u) is H\"older
continuous in u of order greater than 1/2. Our method involves looking at an
associated system of infinite-dimensional stochastic differential equations and
we obtain a uniqueness result for such systems.
