Re: Intersection of sigma-algebras question
From: Tony (Ttiger222_at_hotmail.com)
Date: 01/24/05
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Date: Mon, 24 Jan 2005 12:39:39 -0500
"A N Niel" <anniel@nym.alias.net.invalid> wrote in message
news:240120051253553562%anniel@nym.alias.net.invalid...
> In article <ct30d7$a6kr$1@netnews.upenn.edu>, Tony
> <Ttiger222@hotmail.com> wrote:
>
>> If I have a set X, and two countable subsets C and D of X,
>
> C is a subset of X, not a family of subsets?
>
I'm sorry I meant family C and D are countable families of subsets.
>>
>> then is the sigma
>> algebra generated by (C intersect D) equal to the sigma algebra generated
>> by
>> C, intersected with the sigma algebra generated by D?
>
> Each of these is a sigma-algebra generated by a single set, so
> usually we would not expect C intersect D itself to belong to either
> of the other sigma-algebras.
>
>>
>> If true, would it be ok if C,D are assumed uncountable? If not true,
>> when
>> is this type of equality true?
>>
>> Tony
>>
>>
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