Translates of Sequences for Some Small Sets - Miller, Harry I.; Miller-Van Wieren, Leila (Sarajevo Journal of Mathematics, 2024)
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 otin 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