Definition 0.1. Two representations of groupoids (μ_i,U_G ∗,L_i) , for i = 1, 2 are called equivalent if μ₁ ∼ μ₂, and if there also exists a fiber-preserving isomorphism of analytical Hilbert space bundles v : (U_G ∗

¡/span¿1)—˙U →(U˙G* ˙2)—˙U,whereUisameasurablesubsetofU˙Gofnullcomplementarity; theisomorphismvalsohasthefollowingproperty :v[r(x)]L˙1(x) = L˙2 v[d(x)]forx ∈ G|_U.