PomeDefinition 22.1.34.C172DAF1B3E6 Let $(\Gamma ^ i)_{i\in I}$ be a non-empty family in $\mathrm{PSH}^{\mathrm{NA}}(X,\theta )$. Assume that
Then we define $\operatorname *{sup}_{i\in I}{}\! {}^{*}\Gamma ^ i\in \mathrm{PSH}^{\mathrm{NA}}(X,\theta )$ as the unique element such that for any $\omega \in \textup{Käh}(X)$, we have
\[ \left( \operatorname *{sup}_{i\in I}{}\! {}^{*}\Gamma ^ i \right)^{\theta +\omega }=\operatorname *{sup}_{i\in I}{}\! {}^{*}\Gamma ^{i,\theta +\omega }. \]
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