Definition 0.1
Two
representations
of
groupoids

, for

are called
equivalent if

, and if there also exists a fiber-preserving
isomorphism of analytical Hilbert space bundles

,
where

is a measurable subset of

of null complementarity; the isomorphism

also has the following property:
![$ \hat{v}[r(x)]\hat{L}_1(x) = \hat{L}_2 \hat{v}[d(x)]$](img8.png)
for

.