Skoda–El Mir theorem

The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows:

Theorem (Skoda,^[1] El Mir,^[2] Sibony^[3]). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current ${\displaystyle \Theta }$ on ${\displaystyle X\backslash E}$ which is locally integrable around E. Then the trivial extension of ${\displaystyle \Theta }$ to X is closed on X.