Abstract: Mean-field or McKean-Vlasov type optimal control is closely related to the exciting program of mean-field games. Dynamic programming approach to these control problems result in nonlinear partial differential equations on the space of probability measures. These equations not only require the solution to be differentiable but impose further regularity on the derivatives which are being on the dual of the set of measures are also functions themselves. Despite these difficulties, several approaches to characterize the value function of the control problems as the unique appropriate weak solutions have been developed. In this talk, I discuss a comparison result between sup and super viscosity solutions of the associated dynamic programing equations. Main technical result uses negative Sobolev norms and the classical techniques from the viscosity theory.