I am trying to follow the arguments in page 22 of the following paper k\"{a}hler currents and null loci
It quotes the weak compactness of currents, I wonder if there is any reference about it. My knowledge about currents are all from Demailly's notes
Basically, you can define a norm on the space of $p$ forms, and it will be a Frechet space, then you can talk about weak topology. Does weak compactness mean that the space of currents are weakly compact? If that is true, we also need a way to identify the space of $p$ forms as a subspace of the currents. I guess it can be done through the metric. Is there any reference that actually goes through all these constructions in detail?