Re: Sigma algebra problem
- From: "Konrad Viltersten" <tmp1@xxxxxxxxxxxxxx>
- Date: Thu, 4 Jan 2007 19:45:19 +0100
Let (Omega, F) be a measurable space and pick a sequence
A_1, A_2, ... in F. Now, define B as follows.
B = intersection( n=1, oo, ( union( m=n, oo, A_m ) ) )
How can one show that B is a set of such omegas in Omega
You mean _the_ set of such omega...
I most likely do, hehe.
I think i'll need a clarification on what B looks like. Suppose
we define B_n as follows.
B_n := union( m=n, oo, A_m )
What does it look like if we create a sequence of such B_n's?
I have this feeling that we will get "an eye in an eye"-image,
that is an "area" totally enclosing the next "area", which then
encloses totally the next one, etc.
I think the definition is supposed to exclude some cases, such
as, for instance, a constellation of disjoint islands. However,
i can't kill it myself using that definition.
Does it depend on the fact that
a) it sure is OK to have disjoint islands, or
b) i'm lacking the compentence?
--
Vänligen
Konrad
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Sleep - thing used by ineffective people
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Ambition - a poor excuse for not having
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