Solution
= Solution
For every real $b$,
$$
\boxed{f^{-1}((b,\infty))=\bigcup_{n=1}^\infty f^{-1}([b+1/n,\infty)).}
$$
Each set on the right is measurable by hypothesis. <Closure> of a <sigma-algebra> under countable unions proves the assertion.
= Solution
For every real $b$,
$$
\boxed{f^{-1}((b,\infty))=\bigcup_{n=1}^\infty f^{-1}([b+1/n,\infty)).}
$$
Each set on the right is measurable by hypothesis. <Closure> of a <sigma-algebra> under countable unions proves the assertion.