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The classical Erd{\" o}s-Turan Inequality bounds how far a sequence of pointsin the circle is from being equidistributed in terms of its exponentialmoments. We prove an analogous inequality for all compact simply-connectedsemisimple Lie groups, bounding how far a sequence is from beingequidistributed in the conjugacy classes of the group in terms of the momentsof irreducible characters.

An Erdos-Turan Inequality For Compact Simply-Connected Semisimple Lie Groups