Is it true that if $A \subseteq \mathbb{R}$ is Lebesgue measurable set, then
i) the set $A/2$ is Lebesgue measurable,
ii) the set $-A$ is Lebesgue measurable.
The definition I have for Lebesgue measurability of a set $A$ is: Let $\lambda^*()$ be the Lebesgue outer measure. A set $A$ is called Lebesgue measurable if $\lambda^*(X) = \lambda^*(X \cap A) + \lambda^*(X \cap A^c)$, for any arbitrary set $X$.
I think both are true but I can't show them. A proof sketch or a counter example would be very helpful. Thanks!