Corollary 18.28.14`96B842B9BF11`

Corollary 18.28.14.96B842B9BF11 Let $f\colon K\rightarrow (-\infty ,\infty ]$ be a function bounded from below and $\varphi \in \mathrm{PSH}(X,\theta )_{>0}$ be $\mathcal{I}$-good. Then

\[ P_{\theta ,K}[\varphi ]_{\mathcal{I}}(f)=P_{\theta ,K}[\varphi ](f). \]

Proof. In fact, since $\varphi $ is $\mathcal{I}$-good, a potential $\eta \in \mathrm{PSH}(X,\theta )$ satisfies $\eta \preceq _ P \varphi $ if and only if $\eta \preceq _{\mathcal{I}} \varphi $. Therefore, our assertion follows from corollary 18.28.13 and (18.28.4). $\square$

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@misc{pome-tag-96B842B9BF11,
  author = {{Pome contributors}},
  title = {Corollary 18.28.14},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/96B842B9BF11/}
}

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Corollary 18.28.1496B842B9BF11

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Corollary 18.28.14`96B842B9BF11`