# Should we have a tag for the mean value property of harmonic functions?

A tag named has been created quiterecently. (It is still listed among the new tags.) A tag with the same name was discussed before on meta and rejected: Tag proposal: mean-value-theorem.

However, looking at the questions where the tag-creator added this tag, it seems that the intention was to create a tag for the mean value property of harmonic functions rather than a tag for the mean value theorem from calculus. This raises quite naturally two questions:

• Should we have a separate tag for the mean value property?
• If yes, what should this tag be called?

In any case, using the name mean-value-theorem as the tag for mean value property might lead to confusion. (Most people will recognize result from introductory calculus under this name.) So even if a tag for mean value property is needed, I would suggest using a different name.

EDIT: After this meta post a tag-info was created by the tag-creator (tag-excerpt revisions and tag-wiki revisions).

EDIT2: After the clarification from Guy Fsone that he intended the tag to include both harmonic/complex version and real analysis version, this older question might be related to this discussion as well: Do some calculus theorems deserve to have their own tag?

• I have considered posting in the tag management thread instead, but since the tag started growing relatively quickly, I thought that a separate question might be better, to get a bit more attention to the issue. Sorry for posting two tag-related questions in relatively quick succession and thus hogging a bit more space on meta from other posts. (BTW I have also pinged the tag-creator to let them know about this question.) – Martin Sleziak Nov 23 '17 at 14:58
• Is there a meaning difference between ''mean-value-property'' and mean value theorem.? I think it is same contain. but the appellation differ from authors to another. we can use both appellation as well for me it is ok – Guy Fsone Nov 23 '17 at 15:04
• I did not see the previous tag. But a quick rush to its contain seem like it was dealing only with the one dimensional mean-value-theorem. in my tag I included the higher dimensional cases taylor made for harmonic functions, sub- and sup harmonic functions and complex holomorphic function. I think this is more general – Guy Fsone Nov 23 '17 at 15:09
• It is not more general, @GuyFsone . It's completely different. I suggest using "mean-value-property", if not deleting it. – user99914 Nov 23 '17 at 15:14
• @JohnMa both are ok for me.so.... – Guy Fsone Nov 23 '17 at 15:24
• Can you please stop tagging new question into mean value theorem before we finish this discussion @GuyFsone? Thanks. – user99914 Nov 27 '17 at 20:25
• @Guy: And in case you haven't noticed, you only get one Taxonomist badge. So please stop breaking the tag system. – Asaf Karagila Dec 5 '17 at 12:09
• I will just add that the tag has been recently removed - based on this discussion (and partially also some discussions in chat - see, for example, here, here and here). – Martin Sleziak Dec 6 '17 at 13:14

The mean value property is probably the most characteristic property of harmonic function. Indeed a $C^2$ function is harmonic iff it satisfies the mean value property. Thus if a question is related to mean value property, almost sure the OP will tag "harmonic functions". The only situation I can think of is that student are asked to show the mean value property for holomorphic function. But it seems unlikely that the OP in that situation knows the term "mean value property".
• $p$-harmonic functions, infinite-harmonic functions and the corresponding stochastic games also have mean value properties. – Tommi Dec 5 '17 at 13:01