Abstract
LetE be a Fell bundle over anr-discrete principal groupoid Γ that is measurewise amenable with respect to every quasi-invariant measure on Г (0). LetC * (E) be the correspondingC *-algebra and letC 0(E 0)> be the diagonal subalgebra. The Spectral Theorem on Bimodules proved in this paper gives a description ofC 0(E 0)-bimodules inC * (E).
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