Answer to Question #310729 in Real Analysis for ABC2468

Question

Show that the union of two sets, each of measure zero, has measure zero

Answer 1

By monotonicity and non-negativity of the measure: Let $\mu A=0,\ \mu B=0$:

$0\leq\mu(A\cup B)\leq\mu A+\mu B=0\Rightarrow\mu(A\cup B)=0$