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A General Hewitt-Yosida Decomposition

Published online by Cambridge University Press:  20 November 2018

Tim Traynor
Tim Traynor*
Affiliation:
University of Windsor, Windsor, Ontario
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In 1952, E. Hewitt and K. Yosida [3] proved that a bounded, finitely additive real-valued set function has a unique representation as the sum of a countably additive function and a “purely finitely additive” function.

Below, using a variation of the Carathéodory process we give a suitable generalization to s-bounded vector-valued set functions. In fact, since the methods do not rely on scalar multiplication, we give the result for commutative Hausdorff topological groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1164 - 1169
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Chatterji, S. D., Differentiation along algebras, Manuscripta Math. 4 (1971), 213–224.Google Scholar
2. Dunford, N. and Schwartz, J. T., Linear operators I (Interscience, New York, 1964).Google Scholar
3. Hewitt, E. and Yosida, K., Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46–66.Google Scholar
4. Rickart, C. E., Integration in a convex linear topological space, Trans. Amer. Math. Soc. 52 (1942), 498–521.Google Scholar
5. Rickart, C. E., Decomposition of additive set functions, Duke Math. J. 10 (1943), 653–665.Google Scholar
6. Sion, M., Outer measures with values in a topological group, Proc. London Math. Soc. 19 (1969), 89–106.Google Scholar
7. Sion, M., Lectures on vector-valued measures (Univ. of British Columbia, 1970).Google Scholar
8. Sion, M., Group-valued outer measures (International Congress of Mathematicians, Nice, 1970).Google Scholar
9. Traynor, T., Differentiation of group-valued outer measures, Doctoral Dissertation, Univ. of British Columbia, 1969.Google Scholar
10. Traynor, T., Decomposition of group-valued additive set functions (to appear in Ann. Inst. Fourier 22, 3 (1972)).Google Scholar