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
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 45E
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asap guys
![Α, Β, Α1,...,.
1.2.2: Let u be a measure on an algebra F, and let
..,Ak €F,1<k < m. Then,
(i) (Monotonicity) µ(A) ≤ µ(B) if AC B;
(ii) (Finite subadditivity) μ(A1 U... U Ak) < μ(A1) + ... + μ(Ak);
(iii) (Inclusion-exclusion formula) If μ(A;) < oo for all i = 1,...,k, then
-
μ(AU... Aκ) = Σμ(4) - ΣΜ(ΑΠΑ)
i=1
1<i<j<k
+...+(-1)k−1μ(Α1 Π... Π.Α.).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df4d651-a502-4e9a-93b2-a531f91b18ad%2Fcc208ca3-2949-4121-8249-de22ca76ea0c%2Foq4cf5q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Α, Β, Α1,...,.
1.2.2: Let u be a measure on an algebra F, and let
..,Ak €F,1<k < m. Then,
(i) (Monotonicity) µ(A) ≤ µ(B) if AC B;
(ii) (Finite subadditivity) μ(A1 U... U Ak) < μ(A1) + ... + μ(Ak);
(iii) (Inclusion-exclusion formula) If μ(A;) < oo for all i = 1,...,k, then
-
μ(AU... Aκ) = Σμ(4) - ΣΜ(ΑΠΑ)
i=1
1<i<j<k
+...+(-1)k−1μ(Α1 Π... Π.Α.).
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