19.6.2.8 Measurable functions and sets

Problem: Let \( A_{1}, A_{2} \) be measurable subsequences \( [0 ; 1] \) and \( \mu^{*}\left(A_{1}\right)+\mu^{*}\left(A_{2}\right)>1 \). Prove that \( \mu^{*}\left(A_{1} \cap A_{2}\right)>0 \).