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A decomposition theorem for submeasures

Published online by Cambridge University Press:  18 May 2009

A. R. Khan  and
K. Rowlands
A. R. Khan
Affiliation:
Department of Mathematics, University of MultanPakistan
K. Rowlands
Affiliation:
Department of Pure Mathematics, University College of Wales, Aberystwyth
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In recent years versions of the Lebesgue and the Hewitt-Yosida decomposition theorems have been proved for group-valued measures. For example, Traynor [4], [6] has established Lebesgue decomposition theorems for exhaustive groupvalued measures on a ring using (1) algebraic and (2) topological notions of continuity and singularity, and generalizations of the Hewitt-Yosida theorem have been given by Drewnowski [2], Traynor [5] and Khurana [3]. In this paper we consider group-valued submeasures and in particular we have established a decomposition theorem from which analogues of the Lebesgue and Hewitt-Yosida decomposition theorems for submeasures may be derived. Our methods are based on those used by Drewnowski in [2] and the main theorem established generalizes Theorem 4.1 of [2].

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 69 - 74
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

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