19.6.2.8 Measurable functions and sets

Problem: Let $A_1,A_2$ be measurable subsequences $[0;1]$ and ${\mu }^{\ast }\left(A_1\right)+{\mu }^{\ast }\left(A_2\right)>1$. Prove that ${\mu }^{\ast }(A_1\cap A_2)>0$.