Theorem 9.2 . [03A6]

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Theorem 9.2.

Under the assumptions (A1)–(A3), let $\theta$ be a closed $(1,1)$ -form on ${X^{{\mathrm{an}}}}$ with ample de Rham class. Then for every continuous function $f$ on ${X^{{\mathrm{an}}}}$ with $\theta$ -psh envelope ${P}_{\theta}(f)$ , we have the orthogonality property

\displaystyle\int_{X^{{\mathrm{an}}}}(f-P_{\theta}(f)){\rm MA}_{\theta}(P_{\theta}(f))=0.