The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows: Theorem (Skoda, El Mir, Sibony). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current Θ {\displaystyle \Theta } on X ∖ E {\displaystyle X\backslash E}
which is locally integrable around E. Then the trivial extension of Θ {\displaystyle \Theta } to X is closed on X.
Notes
References J.-P. Demailly, L² vanishing theorems for positive line bundles and adjunction theory, Lecture Notes of a CIME course on "Transcendental Methods of Algebraic Geometry" (Cetraro, Italy, July 1994)