Lusin's Theorem: Let $f$ be a real-valued measurable function on $E$. Then for each $\epsilon > 0$, there is a continuous function $g$ on $\mathbb{R}$ and a closed set $F$ contained in $E$ for which $f=g$ on $F$ and $m(E \setminus F) < \epsilon$.
Now in the exercises: For the function $f$ and the set $F$ in the statement of Lusin's theorem, show that the restriction of $f$ to $F$ is a continuous function.
In Royden's proof, on p. 67 he mentions that $f_n=g_n$ and $f_n \to f$ uniformly on $F$. He goes on to say "the uniform limit of a continuous functions is continuous, so the restriction of $f$ to $F$ is continuous on $F$." Is this question really asking for me to just restate a line from his proof?
