Talk:Σ-algebra: Difference between revisions
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The opening remarks suggest that a sigma algebra satisfies the field axioms - is this true? If so what are the '+' and 'x' operations etc.? |
The opening remarks suggest that a sigma algebra satisfies the field axioms - is this true? If so what are the '+' and 'x' operations etc.? |
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--[[User:SgtThroat|SgtThroat]] 13:08, 10 Nov 2004 (UTC) |
--[[User:SgtThroat|SgtThroat]] 13:08, 10 Nov 2004 (UTC) |
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:I don't think so. The natural operations are union and intersection, and the identities are trivial, but you hit a problem with the inverses' properties of fields. --[[User:Henrygb|Henrygb]] 01:20, 21 Jan 2005 (UTC) |
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Revision as of 01:20, 21 January 2005
Is exist a infinite sigma algebra on an set X such that be countable?
- No, any sigma-algebra is either finite or uncountable. Prumpf 13:14, 12 Oct 2004 (UTC)
The opening remarks suggest that a sigma algebra satisfies the field axioms - is this true? If so what are the '+' and 'x' operations etc.? --SgtThroat 13:08, 10 Nov 2004 (UTC)
- I don't think so. The natural operations are union and intersection, and the identities are trivial, but you hit a problem with the inverses' properties of fields. --Henrygb 01:20, 21 Jan 2005 (UTC)