PomeDefinition 18.28.39.E365D575C322 Let $\mu $ be a Borel probability measure on $K$. We introduce the following functions on $\mathrm{H}^0(X,L^ k \otimes T)$ ($k\geq 1$), with values possibly equal to $\infty $:
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\begin{equation} \begin{aligned} N^ k_{v,\mu }(s) \coloneqq & \left(\int _ K h^ k \otimes h_ T(s,s) \mathrm{e}^{-kv} \, \mathrm{d}\mu \right)^{1/2},\\ N^ k_{v,K}(s) \coloneqq & \sup _{K\setminus \{ v=-\infty \} } \left( h^ k \otimes h_ T(s,s)\mathrm{e}^{-kv}\right)^{1/2}. \end{aligned} \end{equation}
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