Proposition 21.12.20`D60ADA8CEE9B`

Proposition 21.12.20.D60ADA8CEE9B Given $\varphi \in \mathrm{PSH}_{\mathrm{tor}}(X,\omega )$ and $C\in \mathbb {R}$. We have

\[ F_{\varphi +C}=F_{\varphi }+C,\quad G_{\varphi +C}=G_{\varphi }-C. \]

Proof. The first equality follows from (21.12.15). The second is obtained by taking the Legendre transform. $\square$

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BibTeX citation

@misc{pome-tag-D60ADA8CEE9B,
  author = {{Pome contributors}},
  title = {Proposition 21.12.20},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/D60ADA8CEE9B/}
}

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Proposition 21.12.20D60ADA8CEE9B

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Proposition 21.12.20`D60ADA8CEE9B`