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Keywords:
asymptotic density; logarithmic density; $f$-density; continuity
asymptotic density; logarithmic density; $f$-density; continuity
Summary:
The continuity of densities given by the weight functions $n^{\alpha }$, $\alpha \in [-1,\infty [$, with respect to the parameter $\alpha $ is investigated.
References:
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[5] L. Mišík and J. T. Tóth: Logarithmic density of a sequence of integers and density of its ratio set. Journal de Théorie des Nombres de Bordeaux 15 (2003), 309–318. DOI 10.5802/jtnb.404 | MR 2019018
[6] C. T. Rajagopal: Some limit theorems. Amer. J. Math. 70 (1948), 157–166. DOI 10.2307/2371942 | MR 0023930 | Zbl 0041.18301
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