《《测度论讲义习题答案》（严加安）》.pdf

2) μ ( A ? C n 0 )= μ ( A \ C n 0 )+ μ ( C n 0 \ A ) ≤μ ( A \ B )+ μ ( C n 0 \ B ) ≤ε. § 4 4.9 ( ) (?, F ,μ ) ? 0 ??, μ ?(? 0 )= μ(?). ? A ∈F μ ?( A ∩? 0 )= μ ( A ) , μ ?? 0 ∩F μ ?μ (? 0 , ? 0 ∩F ) . 1 0 ? A ∈F μ ?( A ∩? 0 )= μ ( A ). 2 0 μ ?? 0 ∩F (1)? 0 ∩F σ- 2.9 (2) μ ? A = A 1 ∩? 0 = A 2 ∩? 0 ∈? 0 ∩F , A 1 ∩? 0 ∩ A c 2 = ?, ? 0 ?( A 1 \ A 2 ) c . μ ?(? 0 )= μ(?), μ ( A 1 \ A 2)=0. μ ( A 2 \ A 1)=0, μ ( A 1 ? A 2)=0. A 1 = A 2,a.s. (3) μ ?? 0 ∩F μ ?( ?)= μ ?( ?∩? 0 )= μ ( ?)=0. A n ∈F ,n ≥ 1 ,A n ∩ A m = ?,n ?= m , A n ∩? 0 ∈F ,n ≥ 1 , ( A n ∩? 0 ) ∩( A m ∩? 0 )= ?,n ?= m. μ ??∞? n =1 ( A n ∩? 0 ) ?= μ ???∞? n =1 A n ?∩? 0 ?= μ ?∞? n =1 A n ?= ∞? n =1 μ ( A n )= ∞? n =1 μ ?( A n ∩? 0 ) . μ ?? 0 ∩F 4.10 (?, F ,μ ) ? 0 ??. F 0 =? 0 ∩F , ν( A)=inf { μ ( G ): G ∈F ,G ∩? 0 = A } ,A ∈F 0 , 10