Let $f\colon (0,1)\to \mathbb{R}$ be a function continuous on the right, i.e. for any $a\in(0,1)$ one has $\lim_{x\to a+0}f(x)=f(a)$.
Is it true that $f$ is measurable?
I apologize if this question is too elementary for this site.
Let $f\colon (0,1)\to \mathbb{R}$ be a function continuous on the right, i.e. for any $a\in(0,1)$ one has $\lim_{x\to a+0}f(x)=f(a)$.
Is it true that $f$ is measurable?
I apologize if this question is too elementary for this site.