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S.I.P. measures on metrizable groups

Published online by Cambridge University Press:  24 October 2008

C. Karanikas
C. Karanikas
Affiliation:
University of Crete, Heraclion, Greece
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Let G be a metrizable non-discrete locally compact group. Let M(G) be the convolution measure algebra of G. We shall denote by Lx and Rx, x β G, the left and the right translation operation on M(G), respectively. A measure μ β M(G) has strongly independent powers or μ is a s.i.p. measure, if, for x β G and n, m β N,

whenever n ≠ m or x ≠ e, where e is the identity of G. If a measure μ satisfies (1) for x = e and n + m, we say that μ has independent powers, or μ is an i.p. measure. Notice that the powers μn and μm of μ are convolution powers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 511 - 518
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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