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 ⊂ G T \subset G and a natural number M such that G = ∪ t ∈ T t V G = { \cup _{t \in T}}tV and at most M of the tV’s, t ∈ T t \in T , intersect.