Remark 18.28.47129D3B333F18

Remark 18.28.47.129D3B333F18 Recall that in the definition of $\beta ^ k_{v,\varphi ,\mu }$, the singular metric $\varphi $ only appears through the conditions $s \in \mathrm{H}^0(X,L^ k \otimes T \otimes \mathcal{I}(k\varphi ))$. The pointwise norm used to define $\beta ^ k_{v,\varphi ,\mu }$ and $N^ k_{v,\mu }$ is defined via $v$ not $\varphi $.

This leads to the following seemingly paradoxical consequence, if $\psi \in \mathrm{PSH}(X,\theta )$ and $\varphi \preceq _{\mathcal{I}}\psi $, then

We shall apply this consequence without further mention in the sequel.