19.6.2.12 Measurable functions and sets

Problem: Let \( f(x) \leq 0 \) a. e. (almost everywhere) on \( A \) and \( g(x) \leq \) \( \leq 0 \) a. e. on \( A \), let \( h(x)=\max (f(x), g(x)) \). Prove that \( h(x) \leq 0 \) a. e. on \( A \).