Let ${E_{n}}$ be a sequence of Lebesgue measurable sets of real numbers. Prove that the set $A$ of all those points that belong to infinitely many sets from the sequence ${E_{n}}$ is Lebesgue measurable.
Is the proof similar to that of "Borel-Cantelli Lemma"? if yes what will be the difference? If no can anyone provide me with the proof please?
Best Answer
$A=\bigcap_{n=1}^{\infty} \bigcup_{m=n}^{\infty} E_m$ and hence $A$ is measurable.