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Claim 1
.
Let γ \gamma be a closed positive ( 1 , 1 ) (1,1) -current with bounded local potentials over a compact complex manifold X X of complex dimension n n and let φ , ψ ∈ 𝒫 γ \varphi,\,\psi\in{\cal P}_{\gamma} such that 0 ≤ φ ≤ 1 0\leq\varphi\leq 1 and ψ ≤ 0 \psi\leq 0 . Then
∫ X − ψ γ n φ ≤ ∫ X − ψ γ n + n ∫ X γ n . \displaystyle\int\limits_{X}-\psi\,\gamma^{n}_{\varphi}\;\leq\int\limits_{X}-\psi\,\gamma^{n}+n\int\limits_{X}\,\gamma^{n}\,.
(2.2)