Pluripolar set

Summary

A pluripolar set is a subset of $\C^n$ that lies, at least locally, in the set where a plurisubharmonic function takes the value $-\infty$. Pluripolar sets are the negligible sets of pluripotential theory, in the same way as polar sets are the negligible sets of classical potential theory. They have Lebesgue measure zero, and plurisubharmonic functions bounded above extend across closed pluripolar sets. By Josefson's theorem, a set that is pluripolar locally is pluripolar for one plurisubharmonic function on all of $\C^n$.