Sigma algebras are an important tool in analysis, but they also get some special attention in probability theory as "sigma fields". Often students studying probability won't have any real background in measure theory, but will know what a sigma field is.

I would hardly qualify as an expert. I can see this as a reasonable separate tag. (Although I suppose that most, in fact almost all, of questions about sigma-algebras would be also tagged measure-theory.)

Thus I think that sigma-fields is a reasonable synonym of sigma-algebras, but I do not thing that sigma algebra should be automatically linked to measure-theory

I was about to ask whether $\sigma$-rings and similar structures would fall under the same tag, if it is separate again.

There is also an aspect of descriptive set theory and the Borel hierarchy, where measure theory may not really play any role at all.

Do you think it would be useful to ask Willie Wong about his opinion - he created the synonym back than. (I believe at the time he was the moderator who was most active in the tag management.)

@MartinSleziak I'm familiar with the definition of a sigma ring, but that is about where my knowledge on that topic ends.

Ok, perhaps in $\sigma$-structure mentioned in Halmos or any other typical measure theoretic book. But since you've mentioned $\sigma$-fields, it seems that you can see a few more related structures in the same tag.

I am pretty sure that "sigma field" is just what probabilists call "sigma algebras".

Oh, I see.

I had somewhat prematurely removed the sigma-algebras sysn, I restored it.

In any event, I think that sigma algebras are an interesting and diverse enough topic to deserve a tag of their own.

The prematurely because it seems not clear what the exact scope of the sigma tag should.

The ideal would be if the tag was created together with a tag wiki.

@quid Indeed. That is a delicate question.

I restored it to prevent this from getting confused, but I removed it swiftly as soon as there is an alternative agreed upon.

Maybe it could be posted to meta.

@WillieWong In case you happen to be around at some point - what do you think about suggestion to remove the sigma-algebra $\to$ measure-theory synonym? (I thought it might be reasonable to ask you, since you created the synonym.)

@quid I see that in the process you have at least pluralized from sigma-algebra to sigma-algebras. The suggestion to ask about this on meta sounds reasonable.

I did the expectation / expected value stuff.

I'll wait for input on the sigma stuff.

And I'll leave the span for now.

And I won't start the "convex" subject.

Thanks for all the help @Martin, and to @Xander too.

Another thing which might be worth bringing up on meta is spectral-norm vs. matrix-norms - this was brought up in this room recently by John Ma: chat.stackexchange.com/transcript/3740/2018/8/24

Although I am not sure how many tag-related posts should be active on meta at the same time - is seems that questions about tags attract little attention on meta as it is.

Maybe also worth a discussion is an ancient pending syn proposal norm to normed-spaces.

I have downvoted this synonym. I do not recall that it was discussed on meta.

The syn is currently at score $+2$. It seems that this one was suggested quite a long time ago, too.

Maybe after seven years it's about time to decide on it.

I guess it's about time for me to get some sleep. See you later!

I have no strong feelings. I assume this is brought up for good reason (I haven't been checking Meta.Math.SE most of the time). A lot of the synonyms that made sense 6 or 7 years ago no longer make sense. In general I think that if you and/or other current mods thinks it makes sense to un-do synonym mappings that were put-in when I was a mod, you should feel free to go right ahead!

"A lot of the synonyms that made sense 6 or 7 years ago no longer make sense." I should probably qualify this: I meant that sentence in the way that the site has grown so much that 6/7 years ago it may have made sense to just lump all sigma-algebra questions under measure theory so that they get the "exposure" because having too-specialized tags make things hard to organize and searchable; now the site is much bigger it perhaps pays to have more specialized tags so that the opposite is true.

BTW (block-matrices) and (matrices) are separate tags also on MO.

I have asked in Math Meta chat about possible improvements to the tag-wiki for chat: chat.stackexchange.com/transcript/64952/2018/8/26

Since this is (meta) tag related, it's probably worth mentioning here as well.