1.2.2: Let u be a measure on an algebra F, and let A, B, A₁,..., Ak EF, 1 ≤ k <∞o. Then, (i) (Monotonicity) μ(A) ≤μ(B) if AC B; (ii) (Finite subadditivity) (A₁ U...UA) ≤ (A₁)+...+μ(A); (iii) (Inclusion-exclusion formula) If μ(A₁) <∞o for all i = 1,..., k, then k μ(4U...UA») = Σμ(4) - Σ. MADA) i=1 1
1.2.2: Let u be a measure on an algebra F, and let A, B, A₁,..., Ak EF, 1 ≤ k <∞o. Then, (i) (Monotonicity) μ(A) ≤μ(B) if AC B; (ii) (Finite subadditivity) (A₁ U...UA) ≤ (A₁)+...+μ(A); (iii) (Inclusion-exclusion formula) If μ(A₁) <∞o for all i = 1,..., k, then k μ(4U...UA») = Σμ(4) - Σ. MADA) i=1 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.4: Complex Numbers
Problem 61E
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