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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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    @DylanMoreland Thanks for your link!That really helps me.2012-05-05

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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](http://en.wikipedia.org/wiki/Measure_%28mathematics%29#Measures_of_infinite_intersections_of_measurable_sets)2012-05-05