International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 187-188

A note on analytic measures

Nakhle Asmar

Department of Mathematics and Computer Science, California State University, Long Beach, Long Beach 90840, California, USA

Received 24 March 1988; Revised 27 April 1988

Copyright © 1990 Nakhle Asmar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let G be a compact Abelian group with character group X. Let S be a subset of X such that, for some real-valued homomorphism ψ on X, the set Sψ1(],ψ(χ)]) is finite for all χ in X. Suppose that μ is a measure in M(G) such that μˆ vanishes off of S, then μ is absolutely continuous with respect to the Haar measure on G.