並列摘要
For a locally compact groupoid G with a fixed Haar systemλand quasi-invariant measureμ, we introduce the notion ofλ-measurability and construct the space L^1(G, λ, μ) of absolutely integrable functions on G and show that it is a Banach ∗-algebra and a two-sided ideal in the algebraM(G) of complex Radon measures on G. We find correspondences between representations of G on Hilbert bundles and certain class of nondegenerate representations of L^1(G, λ, μ).