Uniformly Distributed Sequences in Locally Compact Groups. II

We consider the following question. When is there a compactification ${G_0}$ of a locally compact group G (recall that a compact group ${G_0}$ is a compactification of G if there is a continuous homomorphism $\phi :G \to {G_0}$ so that $\phi (G)$ is dense in G) with continuous homomorphism $\phi :G \to {G_0}$ with the property that $\{ {g_\nu }\}$ is uniformly distributed in G if and only if $\{ \phi ({g_\nu })\}$ is uniformly distributed in ${G_0}$? Such a compactification ${G_0}$ is called a D-compactification of G. We obtain a solution to this problem and thereby generalize to locally compact groups some results of Berg, Rajagopalan, and Rubel concerning D-compactifications of locally compact abelian groups.