I have a question about the proof of the translation invariance of the Lebesgue outer measure that appears here: <http://mathonline.wikidot.com/translation-invariance-of-the-lebesgue-outer-measure>

[![enter image description here](https://i.stack.imgur.com/75jDl.png)](https://i.stack.imgur.com/75jDl.png)

I don't understand how equation (\*) follows. I also don't understand how equation (\*\*) follows, but if I figured out the first one, I think I would understand it. 

I agree with equation (1) that $m^\*(E+a) \leq \sum\_{n=1}^\infty l(I\_n)$. I also think that from the definition of the outer measure, we have that $m^\*(E) \leq \sum\_{n=1}^\infty l(I\_n)$. But how are they concluding that
$$ m^\*(E+a) \leq m^\*(E)$$ from this information? I think I'm missing something simple, but I've spent several hours thinking about it and can't work it out exactly.