In mathematics, in the area of potential theory, a pluripolar set is the analog of a polar set for plurisubharmonic functions. Definition Let and let be a plurisubharmonic function which is not identically . The set is called a complete pluripolar set. A pluripolar set is any subset of a complete pluripolar set. Pluripolar sets are of Hausdorff dimension at most and have zero Lebesgue measure. If is a holomorphic function then is a plurisubharmonic function. The zero set of is then a pluripolar set. See also Skoda-El Mir theorem References Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992. Potential theory