ScalingStacks

Lemma 3.41 . [02LN]

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Lemma 3.41.

Let H:Qℝ→NℝH\colon Q_{\mathbb{R}}\to N_{\mathbb{R}} be a linear map and gg a concave function on QℝQ_{\mathbb{R}}. If stab⁡(g)∩im⁡(H∨)≠∅\operatorname{stab}(g)\cap\operatorname{im}(H^{\vee})\not=\emptyset then, for all u∈Nℝu\in N_{\mathbb{R}},

supv∈H−1​(u)g⁡(v)<∞.\sup_{v\in H^{-1}(u)}g(v)<\infty.

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