Proposition 1.4 . [032I]

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Proposition 1.4.

Let ${\mathcal{T}}_{[\omega]}(X)$ denote the set of positive closed currents $\omega^{\prime}$ of bidegree $(1,1)$ on $X$ which are cohomologous to $\omega$ . Then

PSH(X,\omega)\simeq{\mathcal{T}}_{[\omega]}(X)\oplus\mathbb{R}.