What does it mean to say that an event is determined by certain random variables? So I was reading Moser and Tardos' paper on their algorithmic proof for the Lovász Local Lemma and came across the following:


  Let $\mathcal{P}$ be a finite collection of mutually independent random variables in a fixed probability space $\Omega$. We will consider events $A$ that are determined by the values of some subset $S \subseteq \mathcal{P}$ of these variables.


(This excerpt was taken from the second paragraph on page 2 of the above mentioned paper.)

What does it mean to say that an event is determined by (the values of) certain random variables? I think it would make sense, for instance, to say that the event $A$ = [$X \neq Y$] is determined by the r.v.s $X$ and $Y$, but I don't know how one would formally write the definition in general.
The event is a function of the random variables.

$A = f(X, Y, Z ...)$ with $X, Y, Z \in S$
The event is a function of the random variables.

$A = f(X, Y, Z ...)$ with $X, Y, Z \in S$