Such a Haar measure is in many cases easy to compute; for example for orthogonal groups it was known to Hurwitz, and in the Lie group cases can always be given by an invariant differential form.
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His research work includes contribution in the field of Group algebra and measure algebra of locally compact group.
Lafforgue was awarded the 2000 EMS Prize for his contribution to the K-theory of operator algebras: the proof of the Baum–Connes conjecture for discrete co-compact subgroups of ,, and some other locally compact group (and of more general objects).