Question

Show by example that even if {An} is a σ−Algebras for every n

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Answer 1

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Answer:}}}}}}}\end{gathered}$

$\implies$Let XX be an infinite set, and AA be the collection of all subsets of XX which are finite or have finite complement. Then AA is an algebra of sets which is not a σσ-algebra.

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Answer 2

Answer:

take X:={a,b,c} and A1:={{a},{b,c},∅,X}, A2:={{b},{a,c},∅,X} and show that A1∪A2 is not a σ-algebra

Explanation:

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