Buck's measure density and sets of positive integers containing arithmetic progression

Milan Paštéka; Tibor Šalát

Mathematica Slovaca (1991)

  • Volume: 41, Issue: 3, page 283-293
  • ISSN: 0139-9918

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Paštéka, Milan, and Šalát, Tibor. "Buck's measure density and sets of positive integers containing arithmetic progression." Mathematica Slovaca 41.3 (1991): 283-293. <http://eudml.org/doc/34321>.

@article{Paštéka1991,
author = {Paštéka, Milan, Šalát, Tibor},
journal = {Mathematica Slovaca},
keywords = {sets of integers; asymptotic density; Buck measure density; - measurable sets; natural density},
language = {eng},
number = {3},
pages = {283-293},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Buck's measure density and sets of positive integers containing arithmetic progression},
url = {http://eudml.org/doc/34321},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Paštéka, Milan
AU - Šalát, Tibor
TI - Buck's measure density and sets of positive integers containing arithmetic progression
JO - Mathematica Slovaca
PY - 1991
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 41
IS - 3
SP - 283
EP - 293
LA - eng
KW - sets of integers; asymptotic density; Buck measure density; - measurable sets; natural density
UR - http://eudml.org/doc/34321
ER -

References

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  1. BUCK R. C., The measure theoretic approach to density, Amer. J. Math. LXVIII (1946), 560-580. (1946) Zbl0061.07503MR0018196
  2. DINCULEANU N., Vector Measures, VEB Deutscher Verlag der Wissen, Berlin, 1966 Zbl0647.60062MR0206189
  3. ERDÖS P., NATHANSON M. B., SÁRKÖZY A., Sumsets containing infinite arithmetic progressions, J. Number Theory 28 (1988), 159-166. (1988) Zbl0633.10047MR0927657
  4. HARDY G. H., WRIGHT E. M., An Introduction to the Theory of Numbers, 3rd ed., Oxford, 1954. (1954) Zbl0058.03301MR0067125
  5. MAHARAM D., Finitely additive measures on the integers, Sankhya: The Indian J, Stat. Ser. A 38 (1976), 44-59. (1976) Zbl0383.60008MR0473132
  6. PAŠTÉKA M., Some properties of Buck's measure density, (To appear.). Zbl0761.11003
  7. SIERPIŃSKI W., Elementary Theory of Numbers, PWN, Warszawa, 1964. (1964) Zbl0122.04402MR0175840
  8. SIKORSKI R., Funkcje rzeczywiste I, PWN, Warszawa, 1958. (1958) MR0105468
  9. SZEMEREDI E., On sets of integers containing no k elements in arithmetic progression, Acta Arithm. 27 (1975), 199-245. (1975) MR0369312

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