If $\{B_n\}_{n=1}^{\infty}$ is a descending collection of sets and $m(B_1)<\infty$, then $m\left(\bigcap\limits_{n=1}^{\infty}B_k\right)=\lim\limits_{k\rightarrow \infty} m(B_k).$
Why is it necessary to have $m(B_1)<\infty$?
If $\{B_n\}_{n=1}^{\infty}$ is a descending collection of sets and $m(B_1)<\infty$, then $m\left(\bigcap\limits_{n=1}^{\infty}B_k\right)=\lim\limits_{k\rightarrow \infty} m(B_k).$
Why is it necessary to have $m(B_1)<\infty$?
Hint: Consider the collection $\{(n,\infty)\}_{n=1}^\infty$.