# Riemann-Stieltjes Integral tag

There are currently separate tags for and , and there have been a couple cases, which were asking about Riemann-Stieltjes integration. I am wondering why is there no riemann-stieltjes-integral tag, and if one should be created?

I wanted to raise the question here before actually creating the tag by myself. Is this a correct thing to do, or I should not trouble the community with such basic issues?

• It is very good that you ask here. You could also have used the dedicated thread math.meta.stackexchange.com/questions/25694/tag-management-2017 or asked in chat chat.stackexchange.com/rooms/3740/tagging But it is also alright to ask a new question. – quid Nov 8 '17 at 19:42
• Is there an actual need for a tag, though? How many questions explicitly deal with this subject? (I don't know, I'm just asking.) – Asaf Karagila Nov 9 '17 at 2:37
• Perhaps it would be a good idea to take a closer look at the whole tags related to integration, and maybe try to "fix them" in some way, since there are many types of integrals, and while "all integration methods are equal, some are more equal than others" (when it comes to tags anyway). – Asaf Karagila Nov 9 '17 at 2:38
• there do seem to be a few – Alexander Gruber Nov 9 '17 at 6:34
• While the Riemann-Stieltjes integral certainly gets less attention than the other two, I think it's important enough to get its own tag. – Reinstate Monica Nov 9 '17 at 6:44
• And while we're at it, should we also have a tag for the Generalized Riemann integral? It's a little bit of a niche subject, but plenty of niche subjects still get their own tag. – Reinstate Monica Nov 9 '17 at 6:52
• @MonstrousMoonshiner If we mean the same thing by generalized Riemann integral (=Henstock–Kurzweil integral), I have suggested a tag for this kind of integral in this answer. The voting on the suggestion reached score +3 so far. – Martin Sleziak Nov 9 '17 at 12:15
• @MartinSleziak Yes, we are referring to the same thing – Reinstate Monica Nov 9 '17 at 17:09
• So am I hearing that it makes sense to create the tag for Riemann-Stieltjes, and there is a question on something else? Can someone closer to admin privileges please create one then, and retag those questions linked by @AlexanderGruber – gt6989b Nov 10 '17 at 0:19
• You can create the tag if you want. While there are >600 questions linked.... retagging seems to be a nontrivail task. @gt6989b – user99914 Nov 10 '17 at 2:50
• There is also such a thing as a Lebesgue–Stieltjes integral (not to mention a generalized-Riemann–Stieltjes integral, not to be confused with the generalized Riemann–Stieltjes integral, which is still based on the Riemann integral but fixes an inadequacy of Stieltjes's original definition), and one might want to ask in general about Stieltjesization (if I may say that) about any notion of integral. Perhaps there should be a #stieltjes-integral tag that, when appropriate, could be used with the other tags? – Toby Bartels Nov 13 '17 at 21:46
• @TobyBartels i like this idea, so use 2 tags to denote riemann-stijeltjes – gt6989b Nov 14 '17 at 17:12
• @TobyBartels Maybe you could post your comment as a separate answer. (So that other users can vote on this suggestion and possible make some comments about advantages or disadvantages of this possibility.) – Martin Sleziak Nov 15 '17 at 12:18
• @Martin Sleziak : Done. – Toby Bartels Nov 15 '17 at 22:37
• I think we'll rename to just stieltjes-integeral. If you care for a taxonmist badge, you could create it somewhere and I'll merge. If not I'll jsut proceed to do it. – quid Nov 25 '17 at 17:41

I put this in a comment, and @Martin Sleziak suggested that I make it an answer, it here it is again (with better formatting):

There is also such a thing as a Lebesgue–Stieltjes integral[^1], and one might want to ask in general about Stieltjesization (if I may say that) about any notion of integral. Perhaps there should be a #stieltjes-integral tag that, when appropriate, could be used with the other tags?

[^1]: Not to mention a generalized-Riemann–Stieltjes integral, based on the generalized Riemann integral. Not to be confused with the generalized Riemann–Stieltjes integral (no hyphen), which is still based on the Riemann integral but fixes an inadequacy of Stieltjes's original definition.

• So if I understand you correctly, the suggestion is to create (stieltjes-integral) tag - which would cover Riemann-Stieltjes, Lebesgue-Stieltjes and some other similar types fo integral. Would we at the same time remove completely the recently created (riemann-stieltjes-integral) tag? Would it be replaced by the two tags - riemann and stieltjes - in the questions about this topic? – Martin Sleziak Nov 16 '17 at 6:36
• When I made my comment, I hadn't realized that the tag had already been created, so maybe it's better not to mess with things now. But I think that most of the time, the #stieltjes-integral tag (I don't know how to make tags become links in comments, but people can click on the links in the previous comment) would be the only one needed. This is because the Stieltjes aspect is the unusual one; the underlying notion of integral is less likely to be important. Of course, when both aspects are important, then one would use both tags. – Toby Bartels Nov 16 '17 at 18:58
• Well, there are only three examples of the new tag so far, so it wouldn't be hard to switch. Of these, the two questions by @Shatabdi Sinha (and edited by John Ma) want help evaluating a Stieltjes integral, so they would need only a #stieltjes-integral tag, just as asking for help evaluating an ordinary integral would not need a #riemann-integration tag. The other question, by EternusVia, is more theoretical, but it doesn't even mention integration. While Stieltjes integration is related, #bounded-variation (or the rarely used #total-variation) would probably be a better tag. – Toby Bartels Nov 16 '17 at 19:35
• I think this is a good idea, and I'd drop the R-S tag. The syntax for tags is [tag:nameofthetag] and for meta tags it is [meta-tag:nameofthetag] Note that it works irrespective to the tag existing or not. thisisnotanexistingtagname – quid Nov 16 '17 at 20:19
• Would it be possible to suggest what would the tag-info of the suggested look like? (The tag-info should contain some basic advice to help other users make decision when to use the tag. And maybe some basic info about the notion, possibly including some links.) If you - or somebody else who knows about this topic @quid - would be willing to include this into the answer, I guess this might help to gain support for the tag from other users. (The suggestion is currently at $+1$.) – Martin Sleziak Nov 17 '17 at 7:17
• @Martin I am not a particular expert on this, but maybe something like: The Stieltjes integral also known as Riemann--Stieltjes integral is a generalization of the Riemann integral. In addition to an integrand it involves an integrator. Use this tag for questions about this integral as well as closely related integrals such as Lebesgue--Stieltjes. // For the 'excerpt the fully wiki could contain an inetegral and a sum to illustrate what this is about more precisely '// The "Riemann" seems to be optional anyway (even if maybe common in English, yet Ithink uncommon in French and German.) – quid Nov 17 '17 at 20:25
• For questions about Stieltjes integrals. Use with other tags as needed to specify Riemann–Stieltjes, Lebesgue–Stieltjes, etc. – Toby Bartels Nov 20 '17 at 4:17
• The Riemann–Stieltjes integral is a generalization of the Riemann integral in which the integrand is integrated with respect to another function, the integrator. The same idea can be used to define the Lebesgue–Stieltjes integral etc. – Toby Bartels Nov 20 '17 at 4:21
• (The previous two comments are suggestions for the except and body of the tag-wiki, respectively.) – Toby Bartels Nov 20 '17 at 4:23
• Will the tag you mentioned also cover notation questions such as the Stieltjes notation taking to mean $\int df(x) = \int f'(x)dx$ ($f'$ integrable) or should that belong to other tags? Example of a question about Stieltjes notation. – Therkel Nov 21 '17 at 20:27
• @Therkel : That question's not very clear (which seems to be why it was closed). One answer interpreted it as being about a Stieltjes integral, so if that answer interpreted the question correctly, then Yes. (And I'd say that the topic in that case is more than just notation, since no conditions on $f$ were specified, so one may not be able to replace $\mathrm{d}(f(x))$ in a Stieltjes integral with $f'(x) \,\mathrm{d}x$ in a non-Stieltjes integral.) – Toby Bartels Nov 25 '17 at 4:25
• Maybe you have noticed, but it is probably worth mentioning that the tag (stieltjes-integral) has been created. I will also add a link to the related conversation in chat. – Martin Sleziak Dec 3 '17 at 15:30