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We study continuous measures on a compact semisimple Lie group using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if is a compact set of continuous measures on there exists a singular measure such that is absolutely continuous with respect to the Haar measure on...
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