What is a measurable set defined in terms of random variables? I was studying Stochastic Approximation and trying to understand the proof of Dvoretzky Stochastic Approximation Theorem when this expression appeared.
The paper can be found here: link
The sentence I am confused about is
$A$ any set in $\mathcal{F}$ the definition of which can be made in terms of $X_1, ..., X_m$.
$A$ is a measurable set and $X_1, ..., X_m$ are all random variables. Is this maybe an outdated expression? Because I have never read or heard it before.