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user 12383
This tag is to be used only when re-tagging highly(!) off-topic questions where none of the actual tags would make sense; all actual tags the questioner has used are removed and something is needed to have some tag, which is enforced by the software, so this tag is used. However note that this tag is also used in the process of moderators deleting tags. Thus a question having this tag does most of the time not mean that somebody found it off-topic.
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concave function with sublinear growth
The negation of your property 3. is called regular variation.
Here is an example of a concave not regularly varying function (taken from this paper by Iksanov and Rösler, p.10) :
Take $$f(x) = 2^{-k} …
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