Interactive Real Analysis
- part of 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.
Context
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
Context
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).