## 7.3. Measures

### Example 7.3.3(a): Outer Measure of Intervals

Since outer measure should be related to 'length' we expect that the outer measure of the empty set is zero. Indeed, that is the case.
Take the open interval
*(-1/n, 1/n)*, whose length is *2/n*. It covers
the empty set, because the empty set is a subset of every set. Therefore
*m ^{*}(O) < 2/n* for all

*n*which implies that

*m*.

^{*}(*) = 0***O**
Now assume that *A B*.
Then every cover of

*is also a cover of*

**B***, but not every cover of*

**A***covers*

**A***. That means that there are more collections to consider when computing*

**B***m*instead of

^{*}(A)*m*, so that the infimum in the first case is smaller than in the second case.

^{*}(B)