19.6.2.6 Measurable functions and sets

Problem: Let \( A \subset(0 ; 1) \). Let's suppose that \( f(x)=\mu^{*}(A \cap \) \( (\sqrt[5]{x} ; 1)) \). Prove that the function \( f(x) \) decreases, and is continuous on the segment \( [0 ; 1] \).