Induced Representation of Topological groupoids

Let $G$ be a locally compact second countable groupoid with a Haar system.

In this article, we introduce the induced representation of $G$ from a continuous unitary representation of a closed wide subgroupoid $H$ with a Haarsystem provided there exists a full equivariant system of measures $\mu=\{\mu^{u}\}_{u\in G^{0}}$ on $G/H$.

We prove some basic properties of induced representation and a theorem on induction in stages.

A groupoid version of Mackey's tensor product theorem is also provided.

We also prove a groupoid version of Frobenius Reciprocity theorem on compact transitive groupoids.