We introduce a natural extension of the wreath product construction to the setting of locally compact groups

and the embedability of the limit measures. In Section 3 we prove the existence of universal distributions on contrac- tible groups. [He]) and the interplay between

Rajagopalan for pointing out the following three errors and for indicating that if one assumes that G is o-compact, then the defective half of the proof of Lemma 2.1 is repaired..

Finally, to prove the theorem we need only construct the desired metric for a locally compact, second countable group G. For

(iv) G is topologically isomorphic to the Bass-Serre fundamental group of a finite connected graph of groups, with compact vertex and edge stabilizers with open inclusions, or has

This is not true (see Proposition 7.6); however their proof can probably be fixed when G is abelian; nevertheless their proof does not yield path-connectedness in the case of

- The LCA group G has the property that every density extends to a bounded linear functional on the space of semi- periodic functions (that is, every density is induced by a measure

Rajagopalan for pointing out the following three errors and for indicating that if one assumes that G is o-compact, then the defective half of the proof of Lemma 2.1 is repaired..

— Using again Lemma 6.3 (ii) the result of Salem [7] and Lemma 6.1 (ii) we see that every group of the from R" X K where K is a compact abelian group, has S-measures provided