Analytic and arithmetic properties of thin sets
John J. F. Fournier, Louis Pigno · Pacific Journal of Mathematics · 1983
Let Z+ and Z~ denote the sets of positive and negative integers respectively.We study relations between various thinness conditions on subsets E of Z + , with particular emphasis on those conditions that imply Z~U£ is a set of continuity.For instance, if E is a Λ(l) set, a /?-Sidon set (for some p < 2), or a ί/C-set, then E cannot contain parallelepipeds of arbitrarily large dimension, and it then follows that Z~UE is a set of continuity; on the other hand there is a set E that is Rosenthal, strong Riesz, and Rajchman, which is not a set of continuity.