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 An and then used the fact that C An to compute m(C).
Perform a similar calculation to compute m(An) 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).