A Simple Proof of a Covering Property of Locally Compact Groups

Abstract

We give a simple proof of the following result of Emerson and Greenleaf. Theorem. Let V be a relatively compact subset with nonvoid interior of a locally compact group G. Then there exist a subset $T \subset G$ and a natural number M such that $G = { \cup _{t \in T}}tV$ and at most M of the tV’s, $t \in T$, intersect.