Let $\overline{L}=(L,h)$ and $\overline{L}^{\prime}=(L^{\prime},h^{\prime})$ be elements of $\widehat{\operatorname{Pic}}^{+}_{C^{0}}(X)$. Then we have the following:

1. (1)

   $\mu_{\overline{L}}\geq 0$ on $X^{\operatorname{an}}$.

2. (2)

   ${\displaystyle\mu_{\overline{L}}(x)=\lim\limits_{\begin{subarray}{c}n\to\infty\\ n\in{\mathbb{N}}(L)\end{subarray}}\frac{\sigma_{\overline{L}^{\otimes n}}(x)}{n}}$ for $x\in X^{\operatorname{an}}$.

3. (3)

   $\mu_{\overline{L}\otimes\overline{L}^{\prime}}(x)\leq\mu_{\overline{L}}(x)+\mu_{\overline{L}^{\prime}}(x)$ for $x\in X^{\operatorname{an}}$.

4. (4)

   If $\overline{L}\simeq\overline{L}^{\prime}$, then $\mu_{\overline{L}}=\mu_{\overline{L}^{\prime}}$ on $X^{\operatorname{an}}$.

5. (5)

   For $n\geq 0$, $\mu_{\overline{L}^{\otimes n}}=n\mu_{\overline{L}}$ on $X^{\operatorname{an}}$.