Given that $f,g:\mathbb{C}\rightarrow \mathbb{C}$ are holomorphic, $A=\{x\in\mathbb{R}:f(x)=g(x)\}$. The minimum requirement for $f=g$ is
$A$ is uncountable
$A$ has positive lebesgue measure
$A$ contains a nontrivial interval
$A=\mathbb{R}$
By identity theorem to be $f=g$ we just need a limit point inside $A$, so If $A$ has positive lebesgue measure then it will contain a interval so which will have one limit point. so $2$ is correct?