Talk:Σ-algebra

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)

Font used for denotion in math papers is not important?

The following sentence was deleted: "σ-algebras are sometimes denoted using capital letters of the Fraktur typeface".

Yes, this typeface is not used in this article, but reading math papers I found, that they are usually denoted using it. I did not know, how it is called and how should these letters be read and hoped to find this out in this article, but failed. I found the name of the typeface in other place and I thought this note will be helpful for other people. But it's considered not important...

BTW, no note, that similar constructions which are closed under finite set operations are usually called algebras (this term obviously appeared before σ-algebras). The article does not contain anything more than a definition copied from MathWorld and trivial examples. But other trivial info is irrelevant here... Cmapm 01:07, 3 Jun 2005 (UTC)

Those examples are not trivial. Some of those examples are simple, and such serve to illustrate the concent. Some other examples listed there are actuallly very important, so not trivial either.

The information you inserted is not trivial either. I said it was "not valuable". Please feel free to put it back. It is just when I read the article as a whole, I found that minor point about the font distracting from the overall concent. But there is of course room for disagreement. Oleg Alexandrov 01:43, 3 Jun 2005 (UTC)

Also, you are more than welcome to add content to this article if you feel it is incomplete. Oleg Alexandrov 01:44, 3 Jun 2005 (UTC)

question

For definition 2 of a sigma algebra, it says that for a sigma-algebra X, if E is in X, then so is the complement of E. Does this mean the complement of E in S (i.e. S-E)? Or the complement of E with some universal set?

Thanks!

It means the former. I will now try to make it more explicit in the article. Oleg Alexandrov 02:53, 23 Jun 2005 (UTC)

Name and history

Where does the name "sigma-algebra" come from? When were sigma-algebras introduced? -- Tobias Bergemann 13:39, 22 July 2005 (UTC)

Notation

I find it somewhat distracting that the notation used in this article, that in sigma-ideal, and that in measureable function, are not in concordance. I'm also unnerved that the usage of X and S in this article is reversed from the common usage I am used to seeing. That is, I'm used to seeing X be the set, and Σ be the collection of subsets, so that (X, Σ) is the sigma-algebra. Sometimes, S is used in place of Σ. Can I flip the notation used here, or will this offend sensibilities?

Also, do we have any article that defines the notation (X, Σ, μ) as a measure space? (I needed a wikilink for this in dynamical system but didn't find one). linas 13:37, 25 August 2005 (UTC)

Actually, I want to harmonize the notation in all three articles. But before doing so, we should agree on a common notation. I propose:

• X be the set
• Σ be the collection of subsets
• E and E_n are the elements of Σ (and leave alone A_n for those articles that already use that).
• μ is the measure.
• (X, Σ) and (Y, T) are the sigma algebras,
• (X, Σ, μ) and (Y, T, ν) are measure spaces.

This change will eliminate/replace the use of F, ${\mathcal {A}}$ and Ω in these three articles. Ugh. Measure (mathematics) is not even self-consistent, switching notation half-way through. linas 13:50, 25 August 2005 (UTC)

Other articles includde:

• Measure-preserving dynamical system