The question goes like this:
Let $(S,\mathscr{S}),(T,\mathscr{T})$ be measurable spaces. Show that $\mathscr{S}\times\mathscr{T}$ is the $\sigma-algebra$ generated by the sets $E\times F$ with $E\in \mathscr{S},F\in \mathscr{T}$.
In other words, $\mathscr{S}\times \mathscr{T}$ is the coarsest σ-algebra on $S\times T$ with the property that the product of a $\mathscr{S}$-measurable set and a $\mathscr{T}$-measurable set is always $\mathscr{S}\times \mathscr{T}$-measurable
I thought that this was just the definition of a product set. So, I'm not really sure where to go from here. Could somebody help me understand what the question is asking?