The set $\PSH(X,\theta)$ is convex. If $\varphi$ is $\theta$-psh and $c\in\mathbf{R}$, then $\varphi+c$ is $\theta$-psh. If $\theta$ is furthermore semipositive, then $\max\{\varphi,\psi\}$ is $\theta$-psh when $\varphi,\psi\in\PSH(X,\theta)$.