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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A uniqueness condition for finite measures


Author: J. E. Nymann
Journal: Proc. Amer. Math. Soc. 108 (1990), 913-919
MSC: Primary 28A10; Secondary 60A10
MathSciNet review: 1000164
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Abstract: Let $ \mu $ and $ \mu '$ be two finite measures on the same measurable space which have the property: $ \mu (A) = \mu (B)$ implies that $ \mu '(A) = \mu '(B)$. If the range of $ \mu $ is an interval, then there is a constant $ \alpha $ such that $ \mu ' = \alpha \mu $. This extends earlier results of Leth and Malitz on purely atomic measures.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1000164-9
PII: S 0002-9939(1990)1000164-9
Article copyright: © Copyright 1990 American Mathematical Society