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Unbounded Vector Measures

Published online by Cambridge University Press:  20 November 2018

William Byers
William Byers*
Affiliation:
McGill University and University of California, Berkeley
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The aim of this paper is to extend the idea of a measure which takes on values in Euclidean n-space so as to allow it to assume infinite values while preserving its countable additivity over a given σ-ring. It is shown that in order to do this it is necessary to restrict the range of the measure to one infinite value.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 3 , August 1966 , pp. 331 - 341
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Liapounoff, A., Sur les fonctions-vecteurs completement additives, Bull. Acad. Sci. URSS Ser. Math. Vol. 4 (1940) 465-478.Google Scholar
2. Halmos, P. R., The range of a vector measure, Bull. A. M. S. vol. 54(1948), 416-421.Google Scholar
3. Halmos, P. R., On the set of values of a finite measure, Bull. A. M.S. vol. 53(1947), 138-144, (lemmas 1 and 2). (Note that the statement and proof of lemma 5 are wrong.)Google Scholar
4. Halmos, P. R., Measure theory. Princeton (1950).Google Scholar
5. Gould, G. G., Integration over vector-valued measures, Proc. Lon. Math. Soc., vol. 15, part 2 (1965), 193-225.Google Scholar