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Proceedings of the American Mathematical Society

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

 
 

 

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: 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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DOI: https://doi.org/10.1090/S0002-9939-1970-0279266-8
Keywords: Atom, purely atomic measure, atomic measure, nonatomic measure, sigma-finite measure, semifinite measure
Article copyright: © Copyright 1970 American Mathematical Society

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