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On the equivalence of the properties of quasi-translation invariance and absolute continuity of measures on a locally compact abelian group

Published online by Cambridge University Press:  24 October 2008

Denis Bell
Denis Bell
Affiliation:
Department of Mathematics, Suffolk University, Beacon Hill, Boston, MA 02114, U.S.A.
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Abstract

We give a simple proof that a measure on a locally compact abelian group G is quasi-translation invariant with continuous translation densities if and only if it is equivalent to Haar measure on G and has a continuous positive density.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 279 - 281
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Bell, D.. On the relationship between differentiability and absolute continuity of measures on ℝn. Probability Theory and Related Fields 72 (1986), 417–424.CrossRefGoogle Scholar
[2]Skorohod, A. V.. Integration in Hilbert space (Springer-Verlag, 1974).CrossRefGoogle Scholar