Prove that for the Lebesgue-measure $\lambda$, the inequality $\lambda(A + B) \ge \lambda(A) + \lambda(B) $ holds. So, this task is divided in some smaller tasks, and I’m supposed to begin with the following one: Show that the inequality holds for half-open intervals $A = [a_1, b_1)$ and $B = [a_2, b_2)$ with $a_1, a_2, […]

Let $G$ be a non-measurable subgroup of $(\mathbb R,+)$ , $I$ be a bounded interval , then is it true that $m^*(G \cap I)=m^*(I)(=|I|)$ ? where $m^*$ denotes the Lebesgue outer measure

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