Let (S,F,u) be a measure space. Let F= {A: B₁ CACB2 for some B₁, B2 E F satisfying μ(B₂\ B₁) = 0). For any A EF, setμ(A) = μ(B₁) = μ(B₂) for any pair of sets B₁, B₂ EF with B₁ CAC B₂and μ(B₂B₁) = 0. Then(i) F is a o-algebra and FCF,(ii) is well defined,(iii) (N, F, μ) is a complete measure space and μ = μ on F.

Answered: Image /qna-images/answer/b48abba8-5dd5-4f49-84fb-0e6f862722c3.jpg

Answered: Let (S,F,u) be a mee e B₁, B2 E F…

Let (S,F,u) be a mee e B₁, B2 E F satisfying (E 1) = μ(B₂) for any pair of B₁) = 0. Then ao-algebra and FCF, ell defined

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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Question

Let (S,F,u) be a measure space. Let F= {A: B₁ CAC
B2 for some B₁, B2 E F satisfying μ(B₂\ B₁) = 0). For any A EF, set
μ(A) = μ(B₁) = μ(B₂) for any pair of sets B₁, B₂ EF with B₁ CAC B₂
and μ(B₂B₁) = 0. Then
(i) F is a o-algebra and FCF,
(ii) is well defined,
(iii) (N, F, μ) is a complete measure space and μ = μ on F.

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