Let $\Phi$ be any psh function on the open subset of $\{1<|\zeta_{i}|<\Lambda,i=1,\ldots n\}\subset(\mathbb{C}^{*})^{n}$. Then the $T^{n}$-invariant function

$$\bar{\Phi}(\log|\zeta_{1}|,\ldots,\log|\zeta_{n}|)=\frac{1}{(2\pi)^{n}}\int_{T^{n}}\Phi(|\zeta_{1}|e^{i\theta_{1}},\ldots|\zeta_{n}|e^{i\theta_{n}})d\theta_{1}\ldots d\theta_{n}$$

is a convex function in the variables $x_{1}=\log|\zeta_{1}|,\ldots,x_{n}=\log|\zeta_{n}|$.