Is the following true for Lebesgue outer measure?
$\forall i\in\mathbb{N}^+,A_i\subseteq \mathbb{R}^n$,then
$m^*(\bigcap_{i\in\mathbb{N}^+}A_i)=\lim_{N\to\infty}m^*(\bigcap_{i=1}^NA_i)$
Is the following true for Lebesgue outer measure?
$\forall i\in\mathbb{N}^+,A_i\subseteq \mathbb{R}^n$,then
$m^*(\bigcap_{i\in\mathbb{N}^+}A_i)=\lim_{N\to\infty}m^*(\bigcap_{i=1}^NA_i)$
No. Take $A_n=[n,\infty)$.
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