  The work concerns the superposition between the Zakai equations and the
Fokker-Planck equations on measure spaces. First, we prove a superposition
principle for the Fokker-Planck equations on $\mR^\mN$ under the integrable
condition. And then by means of it, we show two superposition principles for
the weak solutions of the Zakai equations from the nonlinear filtering problems
and the weak solutions of the Fokker-Planck equations on measure spaces. As a
by-product, we give some weak conditions under which the Fokker-Planck
equations can be solved in the weak sense.
