Timeline for Who was/were the first to note that if $\sum_{x \in X} \frac{1}{x} < \infty$ then the natural density of $X$ is zero?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| S Feb 10, 2016 at 11:36 | history | suggested | Martin Sleziak | CC BY-SA 3.0 |
added link and corrected typo in the name of the author
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| Feb 10, 2016 at 11:24 | review | Suggested edits | |||
| S Feb 10, 2016 at 11:36 | |||||
| Jul 10, 2015 at 8:23 | comment | added | Salvo Tringali | In addition, the full reference to the paper of Kronecker mentioned in the above comments is: L. Kronecker, Quelques remarques sur la détermination des valeurs moyennes, C. R. Math. Acad. Sci. Paris 103 (Nov., 1886), 980-987. The paper is available to download from the website of the Bibliotèque nationale de France (gallica.bnf.fr/ark:/12148/cb343481087/date.r=.langEN). | |
| Jul 10, 2015 at 6:57 | comment | added | Salvo Tringali | For the record, here is the full reference to the papers mentioned in the answer above: J. Krzyś, A theorem of Olivier and its generalizations (in Polish), Prace matem. 2 (1956), 159-164 and L. Moser, On the series $\sum 1/p$, Amer. Math. Monthly 65 (1958), 104-105. @Igor: G. Grekos noted there is a typo in the way the name of Krzyś is spelled in the post, and tried to edit, but I think he can't, since he is not a registered user. | |
| Jul 9, 2015 at 22:25 | review | Suggested edits | |||
| Jul 9, 2015 at 23:33 | |||||
| Jul 9, 2015 at 21:35 | comment | added | Salvo Tringali | Following your hint, I gave a look at Knopp's Theory and Application of Infinite Series (2nd English ed.): The result on the "weighted limit" in your post appears as Theorem 3 in Section 82 (p. 129) of the book, and in a footnote on the same page Knopp provides a reference: L. Kronecker, C. R. Math. Acad. Sci. Paris 103 (1886), p. 980 (no title is provided). This may be the first implicit reference to the result mentioned in the OP, but I am not quite sure/don't know whether the notion of natural density had already been introduced at that time. In any case, +1. | |
| Jul 9, 2015 at 20:47 | history | answered | Igor Rivin | CC BY-SA 3.0 |