Suppose $B$ is a Borel set and $f$ mapping from $B$ to $R$ is a non decreasing function.Prove that $f(B)$ is a Borel set.
f is a Borel measurable function because the inverse image of $(a, \infty)$ will be of the form $(t, \infty)$ or $[t,\infty)\cap B$ which is a Borel set. I cannot define inverse function because it may not be strictly increasing. How do I proceed?