I am reading a tutorial on measure theory and it states: "Given an interval $E = [a, b]$ and a set $S$ of subsets of $E$ which is closed under countable unions, we define the following..."
I was wondering what 'closed under countable unions' meant in this case. Does it mean that $S$ contains every element of $E$?
So if $E = [0,5]$, $S$ could be something like $\{[0,2], [1,3], [2,3], [2,5]\}$ since the union of those would be $[0,5]$... but it would impossible for $S$ to be something like $\{[0,1], [1,4], [2,3]\}$ since the union of those would be $[0,4]$.
Am I correct? Thanks!