Abstract
Let G be a group of homeomorphisms of a locally compact Hausdorff space X onto itself. If for each disjoint pair of compact sets there is a non-empty open set, no image of which meets both of the compact sets simultaneously, then there is a non-trivial regular Borel measure on X which is invariant under the action of G (a Haar measure). In particular if the group is equicontinuous, there exists such a (Haar) measure; in this case, Haar measure is unique if and only if the group is weakly transitive.
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