  We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov
(FPK) equations for probability measures on infinite-dimensional spaces. We
consider infinite-dimensional drifts that admit certain finite-dimensional
approximations. In contrast to most of the previous work on FPK-equations in
infinite dimensions, we include cases with non-constant coefficients in the
second order part and also include degenerate cases where these coefficients
can even be zero. Also a new existence result is proved. Some applications to
Fokker-Planck-Kolmogorov equations associated with SPDEs are presented.
