Lebesgue Measurability of Translated Sets?

[To0ta]

hello

let E,F be subset of R and a in R . show that

If E is Lebesgue measurable, then E+a is Lebesgue measurable ?

 

[micromass]

Hmmm, I think this actually belongs in the homework section...

What have you been trying already?

 

[micromass]

Well, what I would try is considering the following

$$\mathcal{A}=\{E\subseteq \mathbb{R}~\vert~E+a~\text{is Lebesgue measurable}\}$$

and now you only need to show that this is a $$\sigma$$-algebra that contains the open intervals...