I'm quite interested in this topic, but the main text on Several Complex Variables say little of nothing about it. As it happens, you are immediately led to think of conspiracy, when few main texts lack information about something you judge of capital mathematical importance, at least in that very moment. Here are my questions, and I'd be grateful of any reference or information.

Let $\Omega$ be an open subset of $\mathbb{C}^n$ and let $F$ be a family of plurisubharmonic functions on $\Omega.$ We may assume thet these functions are continuous or smooth if we wish; also, I'm particularly interested in $n=2.$

**Q1.** In what convergence can we get a converging subsequence to a plurisubharmonic function?

**Q2.** Are there further special conditions on the family $F$ that ensure compactness in stronger sense?