Is $\underset{n=1}{\overset{\infty}{\cup}}[-n,n]$ measurable?
This is a question on Measure Theory of a previous exam period. I can't understand if it's that easy as I find it, or I'm missing something here. I would answer that this is correct because we know that a countable union of measurable sets is measurable.
This union is obviously equal to the whole real line. And the real line is measurable.