On weighted densities

Rita Giuliano-Antonini; Georges Grekos; Ladislav Mišík

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 947-962
  • ISSN: 0011-4642

Abstract

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The continuity of densities given by the weight functions n α , α [ - 1 , [ , with respect to the parameter α is investigated.

How to cite

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Giuliano-Antonini, Rita, Grekos, Georges, and Mišík, Ladislav. "On weighted densities." Czechoslovak Mathematical Journal 57.3 (2007): 947-962. <http://eudml.org/doc/31174>.

@article{Giuliano2007,
abstract = {The continuity of densities given by the weight functions $n^\{\alpha \}$, $\alpha \in [-1,\infty [$, with respect to the parameter $\alpha $ is investigated.},
author = {Giuliano-Antonini, Rita, Grekos, Georges, Mišík, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {asymptotic density; logarithmic density; $f$-density; continuity; Positive integers; asymptotic denity; logarithmic density; weighted density},
language = {eng},
number = {3},
pages = {947-962},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On weighted densities},
url = {http://eudml.org/doc/31174},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Giuliano-Antonini, Rita
AU - Grekos, Georges
AU - Mišík, Ladislav
TI - On weighted densities
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 947
EP - 962
AB - The continuity of densities given by the weight functions $n^{\alpha }$, $\alpha \in [-1,\infty [$, with respect to the parameter $\alpha $ is investigated.
LA - eng
KW - asymptotic density; logarithmic density; $f$-density; continuity; Positive integers; asymptotic denity; logarithmic density; weighted density
UR - http://eudml.org/doc/31174
ER -

References

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  1. Théorie générale des densités, Rend. Acc. Naz. delle Scienze detta dei XL, Mem. di Matematica, 108 (XIV, 14) (1990), 253–294. (1990) MR1106580
  2. Sequences, Oxford Univ. Press, 1966. (1966) MR0210679
  3. The General Theory of Dirichlet Series, Cambridge Univ. Press, 1952. (1952) 
  4. Sets of positive integers with prescribed values of densities, Mathematica Slovaca 52 (2002), 289–296. (2002) MR1936334
  5. 10.5802/jtnb.404, Journal de Théorie des Nombres de Bordeaux 15 (2003), 309–318. (2003) MR2019018DOI10.5802/jtnb.404
  6. 10.2307/2371942, Amer. J. Math. 70 (1948), 157–166. (1948) Zbl0041.18301MR0023930DOI10.2307/2371942

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