A note on analytic measures (Q914102)

Summary: 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 \(\psi\) on X, the set \(S\cap \psi^{-1}(]-\infty,\psi (\chi)])\) is finite for all \(\chi\) in X. Suppose that \(\mu\) is a measure in M(G) such that \({\hat \mu}\) vanishes off of S, then \(\mu\) is absolutely continuous with respect to the Haar measure on G.