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