Prove that: Suppose $f \colon \Bbb R \rightarrow \Bbb R $, where $f$ is continuous on $(-\infty, 0)$ and on $(0,\infty)$. Show that $f$ is measurable.
Can someone please help me with this proof? My TA told me not to look at it in my self study class because we are not going to cover this. I am trying to understand this although my TA told me not to.
Can someone please give a proof for this. This seems like a good proof to know about continuous and measurbale functions which I might learn later on in another class.