Solution
= Solution
The <density of the rational numbers> gives a countable way to separate two unequal values:
$$
\boxed{\{f<g\}=\bigcup_{q\in\mathbb Q}\bigl(\{f<q\}\cap\{g>q\}\bigr).}
$$
Indeed, $f(x)<g(x)$ holds exactly when some rational number lies strictly between them. Every set inside the union is a <Lebesgue measurable set>, by the definition of a <measurable function> and the closure properties of a <sigma-algebra>. Since $\mathbb Q$ is countable, the union is measurable.