Exercise 8. Let (X,, m) be a measure space and Fed. 2. Prove that the restriction mp of m on a is a measure. 3. Let A be a σ-algebra. The restriction of mon is it a σ-algebra. Is it finite (resp. σ-finite) if m is finite (resp. σ-finite). Exercise 9. Let (X,, m) be a measure space with m(X) <oo. Let (A) c be such that m(A) = m(E), Vn≥ 1. Prove that m(A) m(E). Exercise 8. Let (X,,m) be a measure space and FEA. 2. Prove that the restriction mp of m on 4 is a measure. 3. Let A be a σ-algebra. The restriction of m on B is it a σ-algebra. Is it finite (resp. o-finite) if m is finite (resp. o-finite). Exercise 9. Let (X,,m) be a measure space with m(X) <oo. Let (A) c be such that m(A) = m(E), Vn≥ 1. Prove that m(A) m(E). =