There exists a unique operator

$$(\varphi_{1},\dots,\varphi_{n})\mapsto(\theta+dd^{c}\varphi_{1})\wedge\dots\wedge(\theta+dd^{c}\varphi_{n})$$

taking an $n$-tuple of bounded $\theta$-psh functions to a positive Radon measure on $X$ of mass $\{\theta\}^{n}$ and such that

• •

  the definition is compatible with the definition for $\theta$-psh model functions given in §2.7;

• •

  for any decreasing nets of bounded $\theta$-psh functions $\psi^{j}\to\psi$, and $\varphi_{i}^{j}\to\varphi_{i}$ for $i=1,\dots,n$ we have

  $$\int\psi^{j}\,(\theta+dd^{c}\varphi_{1}^{j})\wedge\dots\wedge(\theta+dd^{c}\varphi_{n}^{j})\longrightarrow\int\psi\,(\theta+dd^{c}\varphi_{1})\wedge\dots\wedge(\theta+dd^{c}\varphi_{n}).$$