Real Analysis student wanting a hint to the following problem:
Let E be a measurable set with m(E) < ∞, and let $\chi_{\small{E}}$ be its characteristic function.
Prove that for any $\epsilon$> 0, there is a step function h(x) such that $m(\{h \neq\chi_{\small{E}}\}) < \epsilon$. Hint: Use the existence of an open set O containing E for which $m(O ∼ E) < \epsilon$.)
I'm struggling to see how to start given the following information...
Thanks!