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It is well-known that for any positive (1,1)-current $T$, there is a decomposition formula according to [Siu74]. That is, $T$ can be written as an infinite sum of prime divisors plus an extra part. In particular, the coefficients can be computed as Lelong numbers. Is there an analogue for an arbitrary (1,1)-current? Since I am not familiar with complex geometry, I hope someone could recommend me a concise relevant reference (apart from Demailly's book because it is a little bit too thick for me).

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