Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T07:29:49.631Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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