PomeTheorem 13.13.11 (Monotonicity theorem).0E5F6133B048 Let $\varphi _ j,\psi _ j\in \mathrm{PSH}(X,\theta _ j)$ for $j=1,\ldots ,n$. Assume that $\varphi _ j \succeq \psi _ j$4 for every $j$, then
\[ \int _{X} \theta _{1,\varphi _1}\wedge \cdots \wedge \theta _{n,\varphi _ n} \geq \int _{X} \theta _{1,\psi _1}\wedge \cdots \wedge \theta _{n,\psi _ n}. \]
In particular, if $\varphi ,\psi \in \mathrm{PSH}(X,\theta )$ with $\varphi \succeq \psi $, then
\[ \int _ X \theta _{\varphi }^ n\geq \int _ X \theta _{\psi }^ n. \]
In other words, the non-pluripolar mass increases as the potentials become less singular.
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