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Apr 7, 2010 at 16:22 comment added Emerton One could add that if $G$ is a reductive Lie group then Harish-Chandra computed the Plancherel measure explicitly (and that this was a very major piece of mathematics!).
Apr 7, 2010 at 16:09 comment added Marty THe $E_\pi$ is a space of endomorphisms. The integral $\int$ is a Hilbert space integral -- the space of $L^2$-sections of a Hilbert space bundle over a measure space. Try looking around for "direct integral of Hilbert spaces" or "spectral measure" to understand better.
Apr 7, 2010 at 16:01 comment added Harry Gindi Is that an end or an integral?
Apr 7, 2010 at 15:58 history answered Marty CC BY-SA 2.5