  We prove a comparison result for viscosity solutions of second order
parabolic partial differential equations in the Wasserstein space. The
comparison is valid for semisolutions that are Lipschitz continuous in the
measure in a Fourier-Wasserstein metric and uniformly continuous in time. The
class of equations we consider is motivated by Mckean-Vlasov control problems
with common noise and filtering problems. The proof of comparison relies on a
novel version of Ishii's lemma, which is tailor-made for the class of equations
we consider.
