ScalingStacks

Definition 8.1 . [01H5]

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Definition 8.1.

The θ\theta-psh envelope Pθ​(u)P_{\theta}(u) of a continuous function u∈C0​(X)u\in C^{0}(X) is defined by setting for each x∈Xx\in X

Pθ(u)(x)=sup{φ(x)∣φ∈PSH(X,θ),φ≤u on X}.P_{\theta}(u)(x)=\sup\left\{\varphi(x)\mid\varphi\in\PSH(X,\theta),\,\varphi\leq u\text{ on }X\right\}.

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