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now i'm studying the skoda el-mir theorem about the extension of a positive closed current $T$. But if $T$ ed $S$ are two positive closed currents on a manifold $X$ such that are equal on $X\setminus A$ where $A$ is an analytic set of $X$ then is it true that $S=T$ on whole $X$? thanks in advance.

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No. Take for example $T=0$ and $S=[A]$ the current of integration over a closed complex analytic hypersurface $A$.

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