From Richard Bass' Real Analysis Text I have the following problem.
Let $m$ be a Lebesgue measure. Suppose for each $n$, $A_n$ is a Lebesgue measurable subset of $[0, 1]$. Let $B$ consist of those points $x$ that is in infinitely many of the $A_n$.
Give an example where $\sum_{n=1}^\infty{m(A_n)} = \infty$, but $m(B) = 0$.
I know that $$B = \limsup{A_n} = \bigcap_{m=1}^\infty\bigcup_{n=m}^\infty{A_n}$$
My question is, can I write the Cantor set, in the same form that $B$ is described in.
If not, I would appreciate hints towards the problem itself.
I think there are some pretty simple examples - much simpler than the Cantor set - with $m(A_n) = 1/n$ and $A_1 \supset A_2 \supset A_3 ... $, in which case the formula for $B$ becomes much simpler too.