On Analytic Multifunctions

For any multifunction $S\subset D_z\times\mathbb{C}_w$, we give a criterion for analyticity (pseudoconcavity) in terms of plurisubharmonicity of the function $V(z,w)=-\ln\rho(w,S_z)$, where $\rho(w,S_a)$ stands for the distance from the point $w$ to the set $S_a=S\cap\{z=a\}$.