19.6.2.11 Measurable functions and sets

Problem: Let \( f_{1}=g_{1} \) and \( f_{2}=g_{2} \) a. e. (almost everywhere) on the set \( A \). Prove that \( f_{1}+f_{2}=g_{1}+g_{2} \) a. e. on the set \( A \).