On analytic multifunctions

For any multifunction S ⊂ D z × ℂ w , we give a criterion for analyticity (pseudoconcavity) in terms of plurisubharmonicity of the function V(z, w) = −lnρ(w, S z ), where ρ(w, S a ) stands for the distance from the point w to the set S a = S ∩ {z = a}.

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