## Measure Theory-Lebesguq Measure

1. The problem statement, all variables and given/known data
Prove the set $$A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} )$$ is Lebesgue measurable and calculate its measure.

2. Relevant equations
3. The attempt at a solution
I've proved the set is measurable...But how can I calculate its measure?

I will be delighted to get some guidance

 Recognitions: Gold Member Science Advisor Staff Emeritus It looks to me like $$A= (\frac{1}{5}, \infty)$$