Definition talk:Sigma-Algebra

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Is there a difference between a sigma-algebra and an algebra of sets? --Prime.mover 22:47, 14 February 2010 (UTC)

I say this mainly as a note that this result needs to be put up, but $\sigma$-algebras are closed under countable unions, whereas algebras are only necessarily closed under finite unions. For example, consider the family of finite & cofinite (finite complement) subsets of $\mathbb N$, say $\Sigma$. This is an algebra. Then $\Sigma$ contains $\set {2 n}$ for each $n \in \N$, but does not contain the union of all such sets, the even natural numbers, since there is neither finitely many even natural numbers (so the set is not finite) nor are there finitely many odd. (so the set is not cofinite) Caliburn (talk) 12:20, 28 April 2022 (UTC)
Is it worth collecting all these definitions of set-of-set collections (algebra of sets, sigma-algebra, delta-algebra, topology, whatever else, including the ur-collection magma of sets) in a neatly-comprehended matrix or something, so the reader will be able to see at a glance exactly what the differences are? --prime mover (talk) 13:11, 28 April 2022 (UTC)
Yes something like the table to the right here would be good. Will look into it eventually. Caliburn (talk) 15:37, 28 April 2022 (UTC)