Vol. 105, No. 1, 1983

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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