/sci/ - Science & Math

how do I show [math]A\subseteq \mathbb{R}[/math] is Lebesgue measurable if and only if [math]A+y[/math] is Lebesgue measurable, for [math]y\in \mathbb{R}[/math]. I know that the outer measure is translation invariant. For instance, [math]m(A+y) = m^{*}(A+y) = m^{*}(A)[/math], but I can't just conclude from this that [math]m(A)[/math] follows, right?