I have this exercise:
Let $\mathscr {S}$ be a collection of subsets of the set $X$. Show that for each $A$ in $\sigma(\mathscr S)$ there is a countable subfamily $\mathscr C_0$ of $\mathscr S$ such that $A\in\sigma(\mathscr C_0)$. $($Hint: Let $\mathscr A$ be the union of the $\sigma$-algebras $\sigma(\mathscr C)$, where $\mathscr C$ ranges over the countable subfamilies of $\mathscr S$, and show that $\mathscr A$ is a $\sigma$-algebra that satisfies $\mathscr S\subset\mathscr A\subset \sigma(\mathscr S)$.$)$
from the book "Measure theory - Donald L. Cohn"
I don't know what $\sigma(...)$ is? Thank you.