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2.5 .
For θ ∈ 𝒵 1 , 1 ( X ) \theta\in\mathcal{Z}^{1,1}(X) we denote by
PSH 𝒟 ( X , θ ) = { f ∈ 𝒟 ( X ) | θ + c 1 ( 𝒪 X , ∥ ∥ triv ⋅ e − f ) ∈ 𝒵 1 , 1 ( X ) is semipositive } {\rm PSH}_{\mathscr{D}}(X,\theta)=\{f\in{\mathscr{D}}(X)\,|\,\theta+c_{1}(\mathcal{O}_{X},{\|\ \|}_{\rm triv}\cdot e^{-f})\in\mathcal{Z}^{1,1}(X)\text{ is semipositive}\}
the set of θ \theta -plurisubharmonic
(θ \theta -psh for short) model functions.
Recall from
[GM16 , Prop. 3.12] that
the set PSH 𝒟 ( X , θ ) {\rm PSH}_{\mathscr{D}}(X,\theta) is stable under the formation
of max.