PomeDefinition 18.1.21.EDCDF35668C4 Let $\varphi _ i\in \mathrm{PSH}(X,\theta _ i)$ for $i=1,\ldots ,n$. Write $T_ i=\theta _ i+\mathrm{dd}^{\mathrm{c}}\varphi _ i$ for each $i=1,\ldots ,n$. Assume that $\operatorname{vol}T_ i>0$ for all $i=1,\ldots ,n$. We define the mixed volume $\operatorname{vol}(T_1,\ldots ,T_ n)$ as follows:
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\begin{equation} \operatorname{vol}(T_1,\ldots ,T_ n)=\int _ X \left(\theta _1+\mathrm{dd}^{\mathrm{c}}P_{\theta _1}[\varphi _1]_{\mathcal{I}}\right)\wedge \dots \wedge \left(\theta _ n+\mathrm{dd}^{\mathrm{c}}P_{\theta _ n}[\varphi _ n]_{\mathcal{I}}\right). \end{equation}
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