Helle Everyone,

In one book, the Lebesgue measure is said to possess the following properties (among others):

1) the measure of any measurable set can be approximated from above by open sets; that is, for any measurable M

$\displaystyle \mu (M) = inf \{ \mu(O): M \subset O, O$ is open $\displaystyle \}$

2) the measure of any measurable set can be approximated from below by compact sets; that is, for any measurable M

$\displaystyle \mu(M) = sup \{ \mu( C ): C \subset M, C $ is compact $\displaystyle \}$

Can any one provide a very simple example of this property? Like in $\displaystyle \mathbb{R}^{1}$?