Take the 2-minute tour ×  If $f$ is a bounded real function on
$[a,b]$, and $f^2 \in \mathscr R$, does it follow that $f \in
\mathscr R$?   share|improve this question add comment  1 Answer
up vote 2 down vote accepted  No. Consider
$$f(x)=\begin{cases}1 & \mbox{if}\quad x\in\mathbb{Q}\\ -1 &
\mbox{if}\quad x\notin\mathbb{Q}\end{cases}$$  share|improve
this answer Thanks, makes perfect sense. –  Ernest Singleton Mar
10 '13 at 0:34 add comment  Your Answer