  We prove a superposition principle for nonlinear Fokker-Planck-Kolmogorov
equations on Euclidean spaces and their corresponding linearized first-order
continuity equation over the space of Borel (sub-)probability measures. As a
consequence, we obtain equivalence of existence and uniqueness results for
these equations. Moreover, we prove an analogous result for stochastically
perturbed Fokker-Planck-Kolmogorov equations. To do so, we particularly show
that such stochastic equations for measures are, similarly to the deterministic
case, intrinsically related to linearized second-order equations on the space
of Borel (sub-)probability measures.
