Proposition 22.1.23`F7D709A21AE1`

Proposition 22.1.23.F7D709A21AE1 Let $\Gamma ,\Gamma '\in \mathrm{PSH}^{\mathrm{NA}}(X,\theta )$. Assume that $\Gamma \leq \Gamma '$. Then

\[ \operatorname{vol}\Gamma \leq \operatorname{vol}\Gamma '. \]

Proof. It suffices to show that for any Kähler form $\omega $ on $X$, we have

\[ \operatorname{vol}\Gamma ^{\theta +\omega }_{-\infty }\leq \operatorname{vol}\Gamma '{}^{\theta +\omega }_{-\infty }, \]

which is an immediate consequence of theorem 13.13.11. $\square$

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BibTeX citation

@misc{pome-tag-F7D709A21AE1,
  author = {{Pome contributors}},
  title = {Proposition 22.1.23},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/F7D709A21AE1/}
}

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Proposition 22.1.23F7D709A21AE1

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Proposition 22.1.23`F7D709A21AE1`