## 7.3. Measures

### Examples 7.3.15(b): Monotone sequences of measurable sets

Find the measure of the Cantor middle-fifth set, i.e. the set obtained
by using a Cantor-set construction but removing the middle-fifth instead of
the middle-third at each stage.

In a previous exercise we computed the measure
of the "regular" Cantor middle-third set. We first computed the measure of sets
*and then used the fact that*

**A**_{n}*to compute*

**C****A**_{n}*m(*.

*)***C**
Perform a similar calculation to compute
*m(A_{n})*
but then use the fact that these sets form a decreasing sequence of sets.

The rest is left as an exercise (the answer is *not* zero).