Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On a problem of Erdős on sequences and measurable sets


Author: K. J. Falconer
Journal: Proc. Amer. Math. Soc. 90 (1984), 77-78
MSC: Primary 28A75; Secondary 11K55
DOI: https://doi.org/10.1090/S0002-9939-1984-0722418-0
MathSciNet review: 722418
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Erdös has conjectured that given a decreasing sequence of real numbers convergent to 0 there always exists a measurable set of positive measure that contains no similar copy of the sequence. We prove this conjecture if the sequence does not converge too rapidly.


References [Enhancements On Off] (What's this?)

  • [1] J. Arias de Reyna, Some results connected with a problem of Erdös. III, Proc. Amer. Math. Soc. 89 (1983), 291-292. MR 712640 (85d:28001)
  • [2] D. Borwein and S. Z. Ditor, Translates of sequences in sets of positive measure, Canad. Math. Bull. 21 (1978), 497-498. MR 523593 (80i:28018)
  • [3] P. Erdös, Problems, Math. Balkanica 4 (1974), 203-204.
  • [4] -, My Scottish Book 'problems', The Scottish Book (R. D. Mauldin, Ed.), Birkhäuser, Boston, Mass., 1981, pp. 35-43. MR 666400 (84m:00015)
  • [5] H. I. Miller, Some results connected with a problem of Erdös. II, Proc. Amer. Math. Soc. 75 (1979), 265-268. MR 532148 (82c:28003)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A75, 11K55

Retrieve articles in all journals with MSC: 28A75, 11K55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0722418-0
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society