Corollary 18.4.5`B853F2E6C70B`

Corollary 18.4.5.B853F2E6C70B If $\theta $ is semipositive and big, then $P_\theta [u]_{\mathcal I}$ has finite extended Monge–Ampère mass for every $u\in \mathrm{PSH}(X,\theta )$.

Proof. By the last identity in corollary 18.4.4, $P_\theta [u]_{\mathcal I}$ is an ordinary model, that is, an envelope fixed point. The mass estimate for envelope fixed points in proposition 16.28.7 applies. $\square$

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BibTeX citation

@misc{pome-tag-B853F2E6C70B,
  author = {{Pome contributors}},
  title = {Corollary 18.4.5},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/B853F2E6C70B/}
}

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Corollary 18.4.5B853F2E6C70B

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Corollary 18.4.5`B853F2E6C70B`