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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

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