Probabilities on contractible locally compact groups: The existence of universal distributions in the sense of W. Doeblin (Q1322929)

Let \(G\) be a locally compact group. In Section 1 the author studies the behaviour of sequences of discrete and continuous convolution semigroups and the embeddability of the limit measures. He considers a generalization of the class of strong root-compact groups (so called \(B\)- root-compact) and proves that infinitely divisible measures on such groups are continuously embeddable up to a shift. A group \(G\) is called contractible if there is \(a \in \Aut (G)\) such that \(a^ n x \to e\), \(x \in G\), \(n \to \infty\). In Section 2 the author gets some results about the structure of contractible groups, and in Section 3 he proves the existence of so-called universal distributions on contractible groups.