Talk:Sigma-additive set function

Merging into measure (mathematics)

Hmmm... I see you've intentionally and knowingly changed this from a redirect to Measure (mathematics) to an independent article, but I don't understand why, since that article also has as its major topic a definition and elementary properties of countable additivity. It's possible that the content here is easier to follow for the uninitiated, but having two definitions in different articles is just asking for them to be expanded in independent, overlapping and confusing ways.

In short, I move that this content be merged back into Measure (mathematics). And if not, the redirects at countable additivity and so forth should probably be changed. —Blotwell 03:08, 27 August 2005 (UTC)[reply]

I created this article because I thought that the topic "sigma additivity" was deserving of its own article. Here are my reasons:

When I follow a link of some term like "sigma additivity", because I want to know what it means, I would rather be sent to an article just about that term, which defines that term right at the top, instead of being directed to an article about a different topic and having to read down into the article, for the definition I'm seeking.
The definition of the property in this article is more general than the one given in Measure (mathematics) (In fact it is not entirely clear to me that you could actually say that Measure (mathematics) actually defines a "sigma additive function", rather it defines a "countably additive measure".)
This article has content which is not now in and does not necessarily belong in Measure (mathematics).
This article has the possibility of expanding further beyond what would necessarily be appropriate for the article Measure (mathematics). For example it could have a section on the history of and motivation of the property. It could describe possible uses of the concept outside of Measure theory. It could explore generalizations or restrictions of the property. It could discuss the relationship between this property and other related properties like subadditivity.

So for these reasons I would prefer to leave this article here. I have, for the time being, redirected countable additivity here. However I really am by no means an expert in this area and I would appreciate, the views of more knowledgeable editors. I will see if I can round some up ;-)

Paul August ☎ 19:03, August 27, 2005 (UTC)

I agree with Paul's reasoning. There is of course some overlap with measure (mathematics) but that's OK. I don't really like super articles containing a lot of stuff when you just want to look up a single thing. That is, I'd vote to keep this article separate. Oleg Alexandrov 22:35, 27 August 2005 (UTC)[reply]

I would be fully convinced into agreeing with you both if I saw evidence that the notion of σ-additivity has application outside the definition of a measure specifically (or at least, outside trivial generalizations thereof). My concern is precisely that has not and cannot have, basically because if you look at the axioms for a measure you'll see that σ-additivity is the only axiom, and hence "σ-additive function" and "measure" are actually the same concept. —Blotwell 04:03, 28 August 2005 (UTC)[reply]