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ABsTRAcr. Let , be a central Borel measure on a compact, connected group G. If 0 is isolated in the range of ,u, then there exists a closed, normal subgroup H of G such that rHp, the restriction of ,A to the cosets of H, is the convolution of an invertible measure with a nonzero idempotent measure. This result extends I. Glicksberg's result for LCA groups. An example is given which shows that this result is false in general for disconnected groups.

Central Fourier-Stieltjes transforms with an isolated value