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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Atomic and nonatomic measures


Author: Roy A. Johnson
Journal: Proc. Amer. Math. Soc. 25 (1970), 650-655
MSC: Primary 28.13
DOI: https://doi.org/10.1090/S0002-9939-1970-0279266-8
MathSciNet review: 0279266
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Abstract | References | Similar Articles | Additional Information

Abstract: Elementary properties of atomic and nonatomic measures are investigated. In addition, it is shown that every measure can be written as the sum of a purely atomic measure and a nonatomic measure. Conditions are given under which this decomposition is unique.


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Keywords: Atom, purely atomic measure, atomic measure, nonatomic measure, sigma-finite measure, semifinite measure
Article copyright: © Copyright 1970 American Mathematical Society