- #1

joypav

- 151

- 0

**Problem:**

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be measurable. Then there exists a sequence of continuous functions $(g_n)$ such that $limg_n(x)$ exists for all $x \in \mathbb{R}$ and $limg_n(x) = f(x)$ a.e. x.

Is this like Lusin's Theorem? Lusin's theorem for the real numbers? If so, how does this change the proof?