Generalization of a result of Borwein and Ditor
Harry I. Miller
Proc. Amer. Math. Soc. 105 (1989), 889-893
Primary 28A05; Secondary 26A21
Full-text PDF Free Access
Similar Articles |
Abstract: D. Borwein and S. Z. Ditor have found a measurable subset of the real line having positive Lebesgue measure and a decreasing sequence of reals converging to zero such that, for each is not in for infinitely many ; thus answering a question of P. Erdös. It will be shown that the result of Borwein and Ditor can be extended using a general -place function in place of plus. Related material is also presented.
Borwein and S.
Z. Ditor, Translates of sequences in sets of positive measure,
Canad. Math. Bull. 21 (1978), no. 4, 497–498.
I. Miller, On certain transformations of sets, Akad. Nauka
Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka 24
(1985), 5–9 (English, with Serbo-Croatian summary). MR 837045
C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in
Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey
of the analogies between topological and measure spaces. MR 584443
- 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)
- H. I. Miller, On certain transformations of sets, Akad. Nauka Umjet. Bosne Hercegov. Rad. LXXVIII, 5-10. MR 837045 (87e:28018)
- J. C Oxtoby, Measure and Category, Springer-Verlag, Berlin and New York, 1970. MR 584443 (81j:28003)
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
© Copyright 1989
American Mathematical Society