Lemma 22.1.1161861C279EAB7

Lemma 22.1.116.1861C279EAB7 Let $\Gamma \in \mathrm{PSH}^{\mathrm{NA}}(X,\theta )$ and $Y\subseteq X$ be an irreducible analytic subset. Then the following are equivalent:

1. C8E4B53ADBE1

   $\Gamma ^{\mathrm{An}}(v_{Y,\mathrm{triv}})\neq -\infty $;

2. 9BDEAFBEB2AD

   $\Gamma ^{\mathrm{An}}|_{Y^{\mathrm{An}}}\not\equiv -\infty $;

3. EB5674CDC803

   $\Gamma $ has a well-defined restriction to $Y$.