# hw5 - Ω . Then F = T θ ∈ Θ F θ is a σ-algebra....

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ECON 831 Homework #5 due in class Nov. 17th Exercise 1: Prove the following statement: If F is an algebra, then (2'): A , B ∈ F ⇒ ( A B ) ∈ F . A collection F of subsets of a non-empty set Ω is an algebra if it satis es: (1) A ∈ F ⇒ A c ∈ F and (2'). Exercise 2: Prove the following statement: Let F θ , θ Θ , be a collection of σ -algebra of subsets of a given set
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Unformatted text preview: Ω . Then F = T θ ∈ Θ F θ is a σ-algebra. Exercise 3: Consider Ω = [-1 , 1] . For n ≥ 1 , de ne F n = ' [-1 , 1] , ∅ , [-1 , 1-1 n 2 ] , (1-1 n 2 , 1] “ . (i) Show that each collection of sets F n is a σ-algebra. (ii) Show that F = S ∞ n =1 F n is not a σ-algebra. 1...
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## This note was uploaded on 02/19/2010 for the course ECON 831 taught by Professor Antoine during the Fall '09 term at Simon Fraser.

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