Let \(X\) be a set, let \(\left(X_{i}, \mathscr{A}_{i}ight), i \in I\), be arbitrarily many measurable spaces and let \(T_{i}: X ightarrow X_{i}\) be a family of maps. Show that a map \(f\) from a measurable space \((F, \mathscr{F})\) to \(\left(X, \sigma\left(T_{i}: i \in Iight)ight)\) is measurable if, and only if, all maps \(T_{i} \circ f\) are \(\mathscr{F} / \mathscr{A}_{i}\)-measurable.