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Absolute Continuity for Group-Valued Measures

Published online by Cambridge University Press:  20 November 2018

Tim Traynor
Tim Traynor*
Affiliation:
University of Windsor, Windsor Ontario
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In this note we generalize the following classical theorem: If μ and ν are finite real-valued measures such that ν(A) = 0 implies μ(A) = 0, then for every ε > 0, there exists δ > 0 such that μ(A)<ε whenever ν(A)< δ.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 577 - 579
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Rickart, C. E., Integration in a convex linear topological space, Trans. Amer. Math. Soc. 52 (1942), 498–521.Google Scholar
2. Sion, M., Outer measures with values in a topological group, Proc. London Math. Soc. (3) 19 (1969), 89–106.Google Scholar
3. Traynor, T., Decomposition of group-valued additive set functions, Ann. Inst. Fourier, 22, 3 (1972), 131–140.Google Scholar