Definition 1.1 . [02D8] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Definition 1.1 .
We let ℰ 1 ( X , ω ) {\mathcal{E}}^{1}(X,\omega) denote the set of ω \omega -psh functions with finite self-energy:
this is the set of functions φ ∈ P S H ( X , ω ) \varphi\in PSH(X,\omega) for which
there exists a sequence φ j ∈ P S H ( X , ω ) ∩ L ∞ ( X ) \varphi_{j}\in PSH(X,\omega)\cap L^{\infty}(X)
such that
φ j ↘ φ and sup j ∫ X ( − φ j ) ( ω + d d c φ j ) n < + ∞ . \varphi_{j}\searrow\varphi\;\;\text{ and }\;\;\sup_{j}\int_{X}(-\varphi_{j})(\omega+dd^{c}\varphi_{j})^{n}<+\infty.