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Contents of PMS, Vol. 14, Fasc. 1,
pages 57 - 62
 

A GENERALIZATION OF KAWADA AND ITÔ’S THEOREM

Peter Eisele

Abstract: For a locally compact group G, a continuous automorphism T , and a probability measure c on G the sequence given by r := cT (c) ...T n- 1(c) n is considered. Under the assumption that the set (T-n : n (- N) is equicontinuous it is shown that (r ) n n (- N converges, and then necessarily to an idempotent probability measure, if and only if the support of c is not contained in a proper coset Hx = xT(H) /= H of a compact subgroup H of G and the support of c is contained in a compact T -invariant subgroup of G.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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