# A problem concerning Lebesgue outer measure

Is the following true for Lebesgue outer measure?

$\forall i\in\mathbb{N}^+,A_i\subseteq \mathbb{R}^n$,then

$$m^*(\bigcap_{i\in\mathbb{N}^+}A_i)=\lim_{N\to\infty}m^*(\bigcap_{i=1}^NA_i)$$

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You might be interested in continuity from above. –  Dylan Moreland May 5 '12 at 5:56
@DylanMoreland Thanks for your link!That really helps me. –  Luqing Ye May 5 '12 at 6:33

No. Take $A_n=[n,\infty)$.

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Dear Alex,thank for your counterexample.Now I think if such extreme situation are deleted ,the conclusion could be true,according to @Dylan Moreland 's link –  Luqing Ye May 5 '12 at 6:39