Geodesic
Measurability of representations of locally compact groups
Sbornik. Mathematics, Tome 186 (1995) no. 2, pp. 245-255

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It is shown that a locally compact group is discrete if and only if all its irreducible unitary representations are weakly Haar-measurable. Furthermore, it is proved that an Abelian locally compact group is discrete if and only if all its characters are measurable. Similar results are obtained for complete Abelian groups and generalized loop groups. 
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     author = {S. V. Lyudkovskii},
     title = {Measurability of representations of locally compact groups},
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S. V. Lyudkovskii. Measurability of representations of locally compact groups. Sbornik. Mathematics, Tome 186 (1995) no. 2, pp. 245-255. http://geodesic.mathdoc.fr/item/SM_1995_186_2_a4/