19.6.1.5 Lebesgue measure and integration

Problem: Let \( f: \mathbb{R} \rightarrow \mathbb{R} \). Prove that \[ \{x \in \mathbb{R}: f(x) \geq c\}=\bigcap_{n=1}^{\infty}\left\{x \in \mathbb{R}: f(x) \geq c-\frac{1}{n}\right\} . \]