Translates of Sequences for Some Small Sets
DOI:
https://doi.org/10.5644/SJM.07.2.06Abstract
D. Borwein and S. Z. Ditor have found a measurable subset $A$ of the real line having positive Lebesgue measure and a decreasing sequence $(d_n)$ of reals converging to $0$ such that, for each $x$, $x+d_n \notin A$ for infinitely many $n$. The set they constructed is nowhere dense. This result prompted us to further explore the question of subsets of $R$ and $R^{2}$ that are of "small size" and the existence of null sequences with the described property and hence attain some related results.
2000 Mathematics Subject Classification. 40D25, 40G99, 28A12
Downloads
References
D. Borwein and S. Z. Ditor, Translates of sequences in sets of positive measure, Canad. Math. Bull., 21 (1978), 497–498.
H.I. Miller and A.J. Ostaszewski, Group action, shift compactness and the KBD theorem, submitted for publication.
