Proposition 16.6.28769D844C274

Proposition 16.6.2.8769D844C274 Given $\varphi ,\psi \in \mathrm{QPSH}(X)$, the following are equivalent:

1. 8350562AE8B9

   For any $k\in \mathbb {Z}_{>0}$, we have

   \[ \mathcal{I}(k\varphi )=\mathcal{I}(k\psi ); \]
2. 799708EE5608

   for any $\lambda \in \mathbb {R}_{>0}$, we have

   \[ \mathcal{I}(\lambda \varphi )=\mathcal{I}(\lambda \psi ); \]
3. F9ADC7F591FD

   for any modification $\pi \colon Y\rightarrow X$ and any $y\in Y$, we have

   \[ \nu (\pi ^*\varphi ,y)=\nu (\pi ^*\psi ,y); \]
4. 3689FC205187

   for any proper bimeromorphic morphism $\pi \colon Y\rightarrow X$ from a Kähler manifold and any $y\in Y$, we have

   \[ \nu (\pi ^*\varphi ,y)=\nu (\pi ^*\psi ,y); \]
5. 5B2C5A6F25AB

   for any prime divisor $E$ over $X$, we have

   \[ \nu (\varphi ,E)=\nu (\psi ,E). \]