Vol. 105, No. 1, 1983

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Analytic and arithmetic properties of thin sets

John J. F. Fournier and Louis Pigno

Vol. 105 (1983), No. 1, 115–141

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 ZE is a set of continuity. For instance, if E is a Λ(1) set, a p-Sidon set (for some p < 2), or a UC-set, then E cannot contain parallelepipeds of arbitrarily large dimension, and it then follows that ZE 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.

Mathematical Subject Classification 2000
Primary: 43A46
Received: 25 February 1981
Revised: 16 February 1982
Published: 1 March 1983
John J. F. Fournier
Louis Pigno