# PlanetPhysics/Equivalent Representations of Groupoids

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}

Two representations of groupoidsFailed to parse (unknown function "\grp"): {\displaystyle (\mu_i, U_{\grp} * \mathbb{H}, L_i)}, for

are called *equivalent* if , and if there also exists a fiber-preserving
isomorphism of analytical Hilbert space bundles **Failed to parse (unknown function "\grp"): {\displaystyle v: (U_{\grp}* \mathbb{H}_1)|_U \longrightarrow (U_{\grp}* \mathbb{H}_2)|_U}**
,
where is a measurable subset of **Failed to parse (unknown function "\grp"): {\displaystyle U_{\grp}}**
of null complementarity; the isomorphism
also has the following property:
for **Failed to parse (unknown function "\grp"): {\displaystyle x \in \grp |_U }**
.