As we know, the outer measure $m^*$ of union of two sets $A$ & $B$ is given by
$m^*(A\cup B)=m^*(A)+m^*(B)-m^*(A\cap B)$. If $A$ and $B$ are disjoint then $m^*(A\cap B)=0$.
Therefore, $m^*(A\cup B)=m^*(A)+m^*(B)$.
Here, $[-1,2]$ and {3} are disjoint. Then
$m^*([-1,2]\cup \{3\})=m^*([-1,2])+m^*(\{3\})$
$=3+0=3$ , because the outer measure of finite set is zero. Is this process correct?
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2Your solution is correct! – cos_dm_math21 Jul 05 '21 at 15:12