Corollary 18.28.64`4CE59F3C4805`

Corollary 18.28.64.4CE59F3C4805 Let $w \in C^0(X)$, $\varphi \in \mathrm{PSH}(X,\theta )$ be a potential with analytic singularities such that $\theta _\varphi $ is a Kähler current. Then

\[ \lim _{k\to \infty }\mathcal{L}_{k,\varphi }(N^ k_{w,X})=\mathcal{E}_{\theta ,X}^{\varphi }(w). \]

Proof. This follows from 18.28.62 and proposition 18.28.59: indeed $\omega ^ n \in \mathrm{BM}(X,0)$, hence $\omega ^ n\in \mathrm{BM}(X,w)$ as $w$ is bounded. $\square$

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@misc{pome-tag-4CE59F3C4805,
  author = {{Pome contributors}},
  title = {Corollary 18.28.64},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/4CE59F3C4805/}
}

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Corollary 18.28.644CE59F3C4805

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Corollary 18.28.64`4CE59F3C4805`