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Definition 17.15.37BDCF69FED30F

Definition 17.15.37.BDCF69FED30F Let $(\Gamma ^ i)_{i\in I}$ be a decreasing net in $\mathrm{TC}(X,\theta )_{>0}$. Assume that

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\begin{equation} \inf _{i\in I}\Gamma ^{i}_{\max }>-\infty , \end{equation}

and

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\begin{equation} \inf _{i\in I} \int _ X \left( \theta +\mathrm{dd}^{\mathrm{c}}\Gamma ^ i_{\tau } \right)^ n>0,\quad \textup{for some }\tau < \inf _{i\in I}\Gamma ^{i}_{\max }. \end{equation}

Then we define $\inf _{i\in I} \Gamma ^{i}\in \mathrm{TC}(X,\theta )_{>0}$ as follows:

  1. 3E567FA790CC

    We set

    \[ \left( \inf _{i\in I} \Gamma ^{i} \right)_{\max }=\inf _{i\in I}\Gamma ^{i}_{\max }; \]
  2. 88EFD81042D1

    for any $\tau < \left( \inf _{i\in I} \Gamma ^{i} \right)_{\max }$, we let

    \[ \left( \inf _{i\in I} \Gamma ^{i} \right)_{\tau }\coloneqq \inf _{i\in I} \Gamma ^{i}_{\tau }. \]
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