My work: To show this, I consider the function $\varphi:E\rightarrow R$ so that $\varphi(E)=\{c_{1},..c_{p}\}$ is a finite set and if $c_{1},..c_{p}$ distnict, then $\varphi = \sum_{j=1}^{p}c_{j}\chi_{E_{j}}$ where $E_{j} = \{\varphi = c_{j}\}$.
I don't how to start the next step. Could you please advice me as possible? Do I need to consider the open intervals? Thanks.