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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online