PomeDefinition 20.1.6.E6F6681E7170 The volume of a pseudo-effective Weil b-divisor $\mathbb {D}$ over $X$ is
\[ \operatorname{vol}\mathbb {D}\coloneqq \lim _{\pi \colon Y\rightarrow X} \operatorname{vol}\mathbb {D}_ Y. \]
The right-hand side is a decreasing net due to proposition 16.6.17, hence the limit always exists. The volume of a non-pseudo-effective Weil b-divisor is defined to be $0$.
We say $\mathbb {D}$ is big if $\operatorname{vol}\mathbb {D}>0$.
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