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Continuous measures on compact Lie groups

M. AnoussisA. Bisbas — 2000

Annales de l'institut Fourier

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

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