Proposition 17.15.34148305D820BC

Proposition 17.15.34.148305D820BC Let $\Gamma \in \mathrm{TC}(X,\theta )_{>0}$ and $\lambda >0$. Then $\lambda \Gamma $ as defined in definition 17.15.33 lies in $\mathrm{TC}(X,\lambda \theta )_{>0}$. Moreover, if $\Gamma \in \mathrm{PSH}^{\mathrm{NA}}(X,\theta )_{>0}$, then $\lambda \Gamma \in \mathrm{PSH}^{\mathrm{NA}}(X,\lambda \theta )_{>0}$.

We have