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Sigma algebra

For a given σ-algebra on a finite state space, can you prove there is a unique partition? (you can assume a partition exists)
Does anybody know how to do this as I'm struggling for ideas.
Reply 1
Avatar for Foxehh
Foxehh
21
Algebra hurts my brain.
Reply 2
Avatar for RichE
RichE
15
Original post by zeeshy
For a given σ-algebra on a finite state space, can you prove there is a unique partition? (you can assume a partition exists)
Does anybody know how to do this as I'm struggling for ideas.

Can't you start with the minimal non-empty sets in the σ-algebra?
Reply 3
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zeeshy
OP
5
Original post by RichE
Can't you start with the minimal non-empty sets in the σ-algebra?

I've started with an empty set but I don't know where to go from there
Reply 4
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zeeshy
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5
Original post by zeeshy
I've started with an empty set but I don't know where to go from there

Actually ignore what I said about the empty set. I've started with a given set but I don't know where to go from here
Reply 5
Avatar for Luwei
Luwei
18
Original post by zeeshy
For a given σ-algebra on a finite state space, can you prove there is a unique partition? (you can assume a partition exists)
Does anybody know how to do this as I'm struggling for ideas.


Do you study maths at university?
Reply 6
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zeeshy
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5
Original post by Luwei
Do you study maths at university?

yes
Reply 7
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RichE
15
Original post by zeeshy
Actually ignore what I said about the empty set. I've started with a given set but I don't know where to go from here

Like I suggested, start with a smallest non-empty set in the algebra.
Reply 8
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zeeshy
OP
5
Original post by RichE
Like I suggested, start with a smallest non-empty set in the algebra.

like {ø,{w1,w2},{w3,w4},Ω}?
Reply 9
Avatar for RichE
RichE
15
Original post by zeeshy
like {ø,{w1,w2},{w3,w4},Ω}?

I've no idea what you mean by that I'm afraid

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